DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND INC
N-30D, 1998-12-11
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DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are  pleased  to  provide  you with this report on the Dreyfus Connecticut
Municipal  Money  Market  Fund, Inc. for the 12-month period ended September 30,
1998.  Your  Fund  produced  a yield of 2.85% and, after taking into account the
effect of compounding, the effective yield was 2.89%.*

The Economy

  The  risk of global recession loomed large by the end of the reporting period.
Since  last  summer,  the international economic crisis has spread from Asia and
Russia  into Latin America and its effects are evident in the U.S., as witnessed
by  early  signs  of  a  slowing  in  our domestic economy. Second-quarter gross
domestic product grew at an annual rate of 1.8%, well below the 5.5% rate in the
first  quarter,  while  the  trade  deficit  has continued to widen, affected by
weakening  foreign  demand  and  low-priced  imports.  These  developments  have
heightened  a  sense  of  global economic interdependence and have resulted in a
shift  in  emphasis by the Federal Reserve Board, whereby fighting inflation has
taken  a subordinate role to that of maintaining stable U.S. economic growth. On
September 29, the Federal Open Market Committee cut interest rates for the first
time  since  January  1996.  That  quarter-point  reduction in the Federal Funds
target rate to 5.25% was designed to cushion the adverse effects of the overseas
economic  crisis on the domestic economy. The Federal Funds rate is the interest
rate that banks charge each other for overnight loans.

  While  the  corporate sector wrestles with the economic implications of global
developments, consumers have powered the economy. The reasons for their optimism
are  no  surprise. Inflation remains tame, running at an annual rate comfortably
below  2% . After-tax income is growing and jobs are plentiful: the unemployment
rate  has  been  at or near 30-year lows throughout the reporting period and new
jobs  have  been  created  at  a  robust pace. The consumer sector comprises two
thirds  of  the  activity in the $8-trillion U.S. economy and, with the business
sector  slowing,  any significant pullback in household spending could trigger a
recession.  Up  to  now,  the spillover effect from developments abroad has been
largely  confined  to the manufacturing sector, whose activity has contracted of
late due to the falloff in export demand. Aside from this "erosion at the edges"
as  Fed  Chairman  Alan  Greenspan  describes  it, layoffs on a broader scale--a
factor that could weaken consumer resolve to spend--so far have not occurred. It
is clear that the Fed is concerned about the possibility of worldwide recession.
The  recent  October  interest rate reduction was a major step by the Fed toward
mitigating the domestic effects of international financial turmoil and a gesture
meant to serve notice to the world of the seriousness of its purpose.

Market Environment/Portfolio Strategy

The Fed's action to reduce the target rate for Fed Funds provided even greater
strength  to  the  short-term  municipal money market. Prior to this action, the
short-term  market  had  already  felt  the  effects of the diminished supply of
eligible  new  issuance  over  the summer months. This year's summer calendar of
municipal  notes (consisting mainly of California paper) was drastically reduced
by  a  combination of factors. Due to the strength of local and state economies,
several issuers reduced the amount of short-term borrowing needed. Additionally,
unlike  prior years, many issuers came to market with securities with maturities
beyond  the 13-month maximum restriction allowable for money funds. Other issues
were  converted  to  a  synthetic  structure that is not currently permitted for
purchase  in  your  Fund. The overall result was a lower yield for most one-year
paper,    both    national    and    state    specific.

  We  extended your Fund's average maturity to the 60-day range in early summer,
just prior to the market strengthening. Your Fund benefited from our purchase of
securities  in  the  one-year  range at yields significantly higher than what is
currently  available  in  the market. In mid-summer, yields began to drop and we
utilized the commercial paper market to maintain the Fund's average maturity. In
the  months  ahead, we will continue to participate in the tax-exempt commercial
paper  market  as  a means of extension while yields in the one-year note market
remain  aggressive.  In  the event of any market weakness, we would consider, if
supply conditions allow, additional purchases of Connecticut-exempt notes in the
one-year  range.  As  always,  we  will structure the portfolio in an attempt to
maximize  current  yield  while  maintaining  our  commitment  to  high  quality
tax-exempt investments.

               Very truly yours,


              [Richard J. Moynihan signature logo]


               Richard J. Moynihan

               Director, Municipal Portfolio Management

               The Dreyfus Corporation

October 16, 1998

New York, N.Y.

* Effective yield is based upon dividends declared daily and reinvested monthly

<TABLE>
DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                   SEPTEMBER 30, 1998

                                                                                                   Principal

Tax Exempt  Investments--96.8%                                                                      Amount           Value
- -------------------------------------------------------

                                                                                                 ____________     _____________
<S>                                                                                           <C>               <C>
Connecticut--84.5%

Town of Berlin, BAN 3.90%, 6/18/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .    $     4,170,000   $     4,177,714

State of Connecticut:

  GO Notes:

       4.5%, Series B, 10/1/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          2,075,000         2,075,000

       4%, Series B, 3/15/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          4,000,000         4,009,135

   Special Tax Obligation Revenue, VRDN (Transportation Infrastructure-1)

       3.55%, (LOC; Commerzbank) (a) . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,700,000        20,700,000

   VRDN 3.90%, (Liquidity; Bayerische Landesbank) (a)  . . . . . . . . . . . . . . . . . .          7,200,000         7,200,000

Connecticut Development Authority, VRDN:

  Health Care Revenue (Corp. for Independent Living Project)

       3.25%, (LOC; Chase Manhattan Bank) (a)  . . . . . . . . . . . . . . . . . . . . . .          8,850,000         8,850,000

   IDR (Blase and Bromley Realty Project) 3.90%, (LOC; Fleet Bank) (a) . . . . . . . . . .          2,880,000         2,880,000

   PCR (Connecticut Light and Power Co. Project)

       3.90%, Series A (Insured; AMBAC and Liquidity; Societe General) (a) . . . . . . . .          8,000,000         8,000,000

   Revenue (Solid Waste Project-Rand/Whitney)

       3.30%, (LOC; Chase Manhattan Bank) (a)  . . . . . . . . . . . . . . . . . . . . . .          2,000,000         2,000,000

Connecticut Health and Educational Facilities Authority, Revenue:

  CP (Yale University):

       3.35%, 11/10/98 (LOC; Yale University)  . . . . . . . . . . . . . . . . . . . . . .          3,600,000         3,600,000

       3.20%, 12/16/98 (LOC; Yale University)  . . . . . . . . . . . . . . . . . . . . . .          4,000,000         4,000,000

       3.40%, 1/22/99 (LOC; Yale University) . . . . . . . . . . . . . . . . . . . . . . .          2,435,000         2,435,000

       3.30%, 2/17/99 (LOC; Yale University) . . . . . . . . . . . . . . . . . . . . . . .          6,000,000         6,000,000

   VRDN:

       (Charlotte Hungerford Hospital) 2.90%, Series C (LOC; Bank of Boston) (a) . . . . .          1,700,000         1,700,000

       Refunding (Bradley Healthcare) 3.20%, Series B (LOC; Fleet Bank) (a)  . . . . . . .          4,730,000         4,730,000

       (Yale University) 3.85%, Series T (LOC; Yale University) (a)  . . . . . . . . . . .          8,500,000         8,500,000

Connecticut Housing Finance Authority, VRDN (Housing Mortgage Finance Program):

   3.80%, Series G (BPA; Morgan Guaranty Trust Co. and Insured; AMBAC) (a) . . . . . . . .          8,565,000         8,565,000

   3.73%, Subseries D-3 (BPA; Landesbank Hessen-Thueringen and Insured; AMBAC) (a) . . . .          9,000,000         9,000,000

Connecticut Special Assessment Second Injury Fund, Revenue, CP:

   3.40%, 11/13/98 (LOC: Credit Agricole-Indosuez and Credit Commercial de Belgique) . . .          5,000,000         5,000,000

   3.40%, 11/24/98 (LOC: Credit Agricole-Indosuez and Credit Commercial de Belgique) . . .          3,000,000         3,000,000

Connecticut Special Assessment Unemployment Compensation Advance Fund, Revenue

  (Connecticut Unemployment)

   3.60%, Series C, 7/1/99 (Insured and Liquidity; FGIC) . . . . . . . . . . . . . . . . .         12,000,000        12,000,000

Town of Fairfield, BAN 3.75%, 11/19/98 . . . . . . . . . . . . . . . . . . . . . . . . . .          3,230,000         3,230,670

Town of New Britain, BAN 3.70%, 4/13/99. . . . . . . . . . . . . . . . . . . . . . . . . .          4,500,000         4,502,302

Town of Redding, BAN 4.10%, 10/22/98 . . . . . . . . . . . . . . . . . . . . . . . . . . .          2,000,000         2,000,443

City of Stamford, BAN 3.90%, 5/17/99 . . . . . . . . . . . . . . . . . . . . . . . . . . .          3,000,000         3,007,203

Stamford Housing Authority, Revenue, VRDN (Morgan Street Project)

   3.65%, (LOC; Deutsche Bank) (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . .          7,500,000         7,500,000

City of Stratford, BAN 4%, 6/16/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .          6,000,000         6,016,376

DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

  STATEMENT OF INVESTMENTS (CONTINUED)                       SEPTEMBER 30, 1998


                                                                                                   Principal

Tax Exempt Investments (continued)                                                                  Amount             Value
- -------------------------------------------------------

                                                                                                 ____________     _____________

U.S Related-12.3%

Commonwealth of Puerto Rico Government Development Bank, CP:

   3.25%, 10/22/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $  3,000,000      $  3,000,000

   3.15%, 12/10/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,000,000

Commonwealth of Puerto Rico Highway and Transportation Authority,

  Transportation Revenue, VRDN

   3.10%, Series A (BPA; Bank of Nova Scotia and Insured; AMBAC) (a) . . . . . . . . . . .          7,300,000         7,300,000

Puerto Rico Industrial, Tourist, Educational, Medical and Environmental Control

  Facilities Financing Authority, Higher Education Revenue, VRDN

   (Ana G. Mendez University Systems Project)
   3.55%, Series A (LOC; Banco Popular de Puerto Rico) (a)   . . . . . . . . . . . . . . .          7,200,000         7,200,000

                                                                                                                 ______________

TOTAL INVESTMENTS (cost $177,178,843). . . . . . . . . . . . . . . . . . . . . . . . . . .              96.8%      $177,178,843

                                                                                                      =======    ==============


CASH AND RECEIVABLES (NET) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .               3.2%    $    5,899,508

                                                                                                      =======    ==============

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             100.0%      $183,078,351

                                                                                                      =======    ==============


Summary of Abbreviations
- -----------------------------------------------------------------------------

AMBAC       American Municipal Bond Assurance Corporation           GO          General Obligation

BAN         Bond Anticipation Notes                                 IDR         Industrial Development Revenue

BPA         Bond Purchase Agreement                                 LOC         Letter of Credit

CP          Commercial Paper                                        PCR         Pollution Control Revenue

FGIC        Financial Guaranty Insurance Company                    VRDN        Variable Rate Demand Notes


Summary of Combined Ratings (Unaudited)
- -----------------------------------------------------------------------------

Moody's                          or                          Standard & Poor's               Percentage of Value

________                                                     _________________               ___________________

VMIG1/MIG1,P1                                                SP1+/SP1, A1+/A1, A2                 79.1%

Not Rated (b)                                                Not Rated (b)                         20.9

                                                                                                 _______

                                                                                                 100.0%

                                                                                                 =======



Notes to Statement of Investments:
- -----------------------------------------------------------------------------

(a)   Securities  payable on demand. Variable interest rate--subject to periodic
      change.

(b)   Securities  which,  while  not rated by Moody's and Standard & Poor's have
      been  determined  by  the  Manager  to  be  of comparable quality to those
      rated securities in which the Fund may invest.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                        SEPTEMBER 30, 1998

                                                                                                     Cost             Value

                                                                                                _____________    ______________
<S>                                                                                              <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments . .     $177,178,843      $177,178,843

                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .                            5,053,460

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                              962,028

                                 Prepaid expenses  . . . . . . . . . . . . . . . . . . . .                               17,265

                                                                                                                 ______________

                                                                                                                    183,211,596

                                                                                                                 ______________


LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                               74,526

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                               58,719

                                                                                                                 ______________

                                                                                                                        133,245

                                                                                                                 ______________


NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $183,078,351

                                                                                                                 ==============



REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                         $183,112,782

                                 Accumulated net realized gain (loss) on investments . . .                              (34,431)

                                                                                                                 ______________



NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $183,078,351

                                                                                                                 ==============


SHARES OUTSTANDING

(1 BILLION SHARES OF $.001 PAR VALUE COMMON STOCK AUTHORIZED). . . . . . . . . . . . . . .                         $183,112,782


NET ASSET VALUE, offering and redemption price per share . . . . . . . . . . . . . . . . .                                $1.00

                                                                                                                         ======




                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                         YEAR ENDED SEPTEMBER 30, 1998

INVESTMENT INCOME
<S>                                                                                         <C>                    <C>
INCOME                           Interest Income . . . . . . . . . . . . . . . . .                                 $6,697,555

EXPENSES:                        Management fee--Note 2(a) . . . . . . . . . . . .          $   956,113

                                 Legal fees  . . . . . . . . . . . . . . . . . . .              291,635

                                 Shareholder servicing costs--Note 2(b)  . . . . .              291,014

                                 Auditing fees . . . . . . . . . . . . . . . . . .               29,057

                                 Custodian fees  . . . . . . . . . . . . . . . . .               17,579

                                 Registration fees . . . . . . . . . . . . . . . .               15,412

                                 Prospectus and shareholders' reports  . . . . . .               14,767

                                 Directors' fees and expenses--Note 2(c) . . . . .                8,519

                                 Miscellaneous . . . . . . . . . . . . . . . . . .                2,506

                                                                                           ____________

                                        Total Expenses . . . . . . . . . . . . . .            1,626,602

                                 Less--reduction in management fee due to

                                    undertaking--Note 2(a) . . . . . . . . . . . .             (382,560)

                                                                                           ____________


                                        Net Expenses . . . . . . . . . . . . . . .                                  1,244,042

                                                                                                                 ____________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                  5,453,513

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b) . . . . . . . . . . . . . . . .                                       (573)

                                                                                                                 ____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . .                                 $5,452,940

                                                                                                                 ============


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                                                       Year Ended           Year Ended

                                                                                   September 30, 1998   September 30, 1997

                                                                                   __________________   ___________________
<S>                                                                                    <C>                   <C>
OPERATIONS:

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . . . . . .       $    5,453,513        $    5,449,449

   Net realized gain (loss) on investments . . . . . . . . . . . . . . . . . . .                 (573)               44,698

                                                                                       ______________        ______________

       Net Increase (Decrease) in Net Assets Resulting from Operations . . . . .            5,452,940             5,494,147

                                                                                       ______________        ______________


DIVIDENDS TO SHAREHOLDERS FROM:

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . . . . . .           (5,453,513)           (5,449,449)

                                                                                       ______________        ______________


CAPITAL STOCK TRANSACTIONS ($1.00 per share):

   Net proceeds from shares sold . . . . . . . . . . . . . . . . . . . . . . . .          316,997,029           237,558,939

   Dividends reinvested  . . . . . . . . . . . . . . . . . . . . . . . . . . . .            5,209,218             5,206,544

   Cost of shares redeemed . . . . . . . . . . . . . . . . . . . . . . . . . . .         (321,057,785)         (250,907,105)

                                                                                       ______________        ______________

       Increase (Decrease) in Net Assets from Capital Stock Transactions . . . .            1,148,462            (8,141,622)

                                                                                       ______________        ______________

          Total Increase (Decrease) in Net Assets  . . . . . . . . . . . . . . .            1,147,889            (8,096,924)


NET ASSETS:

   Beginning of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          181,930,462           190,027,386

                                                                                       ______________        ______________

   End of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         $183,078,351          $181,930,462

                                                                                       ==============        ==============





                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS

  Contained  below is per share operating performance data for a share of Common
Stock  outstanding,  total  investment  return, ratios to average net assets and
other  supplemental  data  for  each period indicated. This information has been
derived from the Fund's financial statements.


                                                                                   Year Ended September 30,

                                                                    ___________________________________________________________


PER SHARE DATA:                                                     1998         1997         1996         1995          1994

                                                                    ______      ______       ______       ______        ______
<S>                                                                 <C>          <C>          <C>          <C>           <C>
   Net asset value, beginning of period  . . . . . . . . . .        $1.00        $1.00        $1.00        $1.00         $1.00

                                                                    ______      ______       ______       ______        ______

   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . .         .029         .029         .029         .033          .023

                                                                    ______      ______       ______       ______        ______

   Distributions:

   Dividends from investment income--net . . . . . . . . . .         (.029)      (.029)       (.029)       (.033)        (.023)

                                                                    ______      ______       ______       ______        ______

   Net asset value, end of period  . . . . . . . . . . . . .         $1.00       $1.00        $1.00        $1.00         $1.00

                                                                    ======      ======       ======       ======        ======


TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . .          2.89%       2.93%        2.94%        3.35%         2.33%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . .           .65%        .65%         .63%         .45%          .22%

   Ratio of net investment income
       to average net assets . . . . . . . . . . . . . . . .          2.85%       2.89%        2.90%        3.31%         2.30%

   Decrease reflected in above expense ratios
       due to undertakings by the Manager  . . . . . . . . .           .20%        .04%         .03%         .18%          .42%

   Net Assets, end of period (000's Omitted) . . . . . . . .      $183,078    $181,930     $190,027     $232,932      $242,067

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

  Dreyfus  Connecticut  Municipal  Money  Market  Fund,  Inc.  (the  "Fund" ) is
registered under the Investment Company Act of 1940, as amended (the "Act") as a
non-diversified  open-end  management  investment company. The Fund's investment
objective  is to provide investors with as high a level of current income exempt
from  Federal  and  State  of Connecticut income taxes as is consistent with the
preservation   of   capital  and  the  maintenance  of  liquidity.  The  Dreyfus
Corporation (the "Manager") serves as the Fund's investment adviser. The Manager
is  a  direct subsidiary of Mellon Bank, N.A. Premier Mutual Fund Services, Inc.
is  the distributor of the Fund's shares, which are sold to the public without a
sales charge.

  It  is the Fund's policy to maintain a continuous net asset value per share of
$1.00; the Fund has adopted certain investment, portfolio valuation and dividend
and distribution policies to enable it to do so. There is no assurance, however,
that  the  Fund  will  be able to maintain a stable net asset value per share of
$1.00.

  The  Fund' s  financial  statements  are prepared in accordance with generally
accepted accounting principles which may require the use of management estimates
and assumptions. Actual results could differ from those estimates.

  (A)  PORTFOLIO  VALUATION:  Investments  in securities are valued at amortized
cost,  which  has  been determined by the Fund's Board of Directors to represent
the fair value of the Fund's investments.

(B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities transactions are
recorded  on  a  trade date basis. Interest income, adjusted for amortization of
premiums  and original issue discounts on investments, is earned from settlement
date and recognized on the accrual basis. Realized gain and loss from securities
transactions  are  recorded  on  the  identified cost basis. Cost of investments
represents  amortized cost. Under the terms of the custodian agreement, the Fund
received  net  earnings  credits of $8,235 during the period ended September 30,
1998  based on available cash balances left on deposit. Income earned under this
arrangement is included in interest income.

  The  Fund  follows  an  investment  policy of investing primarily in municipal
obligations  of  one  state. Economic changes affecting the state and certain of
its  public  bodies  and municipalities may affect the ability of issuers within
the  state to pay interest on, or repay principal of, municipal obligations held
by the Fund.

  (C)  DIVIDENDS  TO  SHAREHOLDERS:   It  is  the  policy of the Fund to declare
dividends  daily  from  investment  income-net. Such dividends are paid monthly.
Dividends  from  net  realized  capital  gain  are  normally  declared  and paid
annually, but the Fund may make distributions on a more frequent basis to comply
with  the  distribution  requirements  of  the Internal Revenue Code of 1986, as
amended (the "Code"). To the extent that net realized capital gain can be offset
by  capital loss carryovers, it is the policy of the Fund not to distribute such
gain.

  (D)  FEDERAL INCOME TAXES: It is the policy of the Fund to continue to qualify
as a regulated investment company, which can distribute tax exempt dividends, by
complying  with the applicable provisions of the Code, and to make distributions
of  income  and  net  realized  capital  gain  sufficient  to  relieve  it  from
substantially all Federal income and excise taxes.

  The  Fund  has  an  unused  capital  loss  carryover  of approximately $34,000
available  for  Federal  income  tax  purposes  to be applied against future net
securities  profits,  if  any,  realized  subsequent  to September 30, 1998. The
carryover  does not include net realized securities losses from November 1, 1997
through  September  30, 1998 which are treated, for Federal income tax purposes,
as arising in fiscal 1999. If not applied, the carryover expires in fiscal 2004

At September 30, 1998, the cost of investments for Federal income tax purposes
was substantially the same as the cost for financial reporting purposes (see the
Statement of Investments).

DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

NOTE 2--MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:

(A) Pursuant to a management agreement with the Manager, the management fee is
computed  at  the  annual  rate  of .50 of 1% of the value of the Fund's average
daily net assets and is payable monthly. The Manager had undertaken from October
1,  1997  through  September  30, 1998, to reduce the management fee paid by the
Fund,  to  the  extent  that  the Fund's aggregate annual expenses, exclusive of
taxes, brokerage, interest on borrowings and extraordinary expenses, exceeded an
annual  rate  of  .65 of 1% of the value of the Fund's average daily net assets.
The  reduction  in  management  fee,  pursuant  to  the undertaking, amounted to
$382,560 during the period ended September 30, 1998.

  (B)  Under  the Shareholder Services Plan, the Fund reimburses Dreyfus Service
Corporation,  a  wholly-owned subsidiary of the Manager, an amount not to exceed
an  annual rate of .25 of 1% of the value of the Fund's average daily net assets
for certain allocated expenses of providing personal services and/or maintaining
shareholder  accounts.  The  services  provided  may  include  personal services
relating  to  shareholder  accounts,  such  as  answering  shareholder inquiries
regarding  the  Fund  and  providing reports and other information, and services
related  to  the  maintenance  of  shareholder accounts. During the period ended
September  30,  1998,  the Fund was charged $194,596 pursuant to the Shareholder
Services Plan.

  The  Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,   under  a  transfer  agency  agreement  for  providing  personnel  and
facilities  to  perform transfer agency services for the Fund. During the period
ended September 30, 1998, the Fund was charged $58,871, pursuant to the transfer
agency agreement.

  (C)  Each  director  who  is  not an "affiliated person" as defined in the Act
receives  from  the  Fund  an  annual fee of   $1,000. The Chairman of the Board
receives an additional 25% of such compensation.


DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF DIRECTORS

DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.


  We  have  audited  the  accompanying  statement  of  assets and liabilities of
Dreyfus  Connecticut  Municipal Money Market Fund, Inc., including the statement
of  investments,  as  of  September  30,  1998,  and  the  related  statement of
operations  for  the year then ended, the statement of changes in net assets for
each  of  the  two  years in the period then ended, and financial highlights for
each  of  the  years indicated therein. These financial statements and financial
highlights  are  the responsibility of the Fund's management. Our responsibility
is  to express an opinion on these financial statements and financial highlights
based on our audits.

  We  conducted  our  audits  in  accordance  with  generally  accepted auditing
standards.  Those standards require that we plan and perform the audit to obtain
reasonable  assurance  about  whether  the  financial  statements  and financial
highlights  are free of material misstatement. An audit includes examining, on a
test  basis,  evidence  supporting  the amounts and disclosures in the financial
statements  and  financial  highlights.  Our procedures included confirmation of
securities owned as of  September 30, 1998 by correspondence with the custodian.
An  audit also includes assessing the accounting principles used and significant
estimates  made  by  management,  as  well  as  evaluating the overall financial
statement  presentation.  We  believe that our audits provide a reasonable basis
for our opinion.

  In  our opinion, the financial statements and financial highlights referred to
above  present  fairly,  in  all  material  respects,  the financial position of
Dreyfus Connecticut Municipal Money Market Fund, Inc. at September 30, 1998, the
results of its operations for the year then ended, the changes in its net assets
for each of the two years in the period then ended, and the financial highlights
for  each  of  the  indicated  years,  in  conformity  with  generally  accepted
accounting    principles.



New York, New York

November 6, 1998

IMPORTANT TAX INFORMATION (UNAUDITED)

  In  accordance  with  Federal  tax  law,  the  Fund  hereby designates all the
dividends paid from investment income-net during the fiscal year ended September
30, 1998 as "exempt-interest dividends" (not subject to regular Federal and, for
individuals who are Connecticut residents, Connecticut personal income taxes).


[dreyfus lion "d" logo]                                   (reg.tm)

[dreyfus logo]                                   (reg.tm)

DREYFUS CONNECTICUT MUNICIPAL

MONEY MARKET FUND, INC.

200 Park Avenue

New York, NY 10166

MANAGER

The Dreyfus Corporation

200 Park Avenue

New York, NY 10166

CUSTODIAN

The Bank of New York

90 Washington Street

New York, NY 10286

TRANSFER AGENT &

DIVIDEND DISBURSING AGENT

Dreyfus Transfer, Inc.

P.O. Box 9671

Providence, RI 02940



Printed in U.S.A.                                              101AR989

Connecticut

Municipal Money

Market Fund

Annual Report

September 30, 1998



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