DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND INC
N-30D, 1996-11-22
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DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on the Dreyfus Connecticut
Municipal Money Market Fund, Inc. For its annual reporting period ended
September 30, 1996, your Fund provided an annualized yield of 2.89%. Income
dividends exempt from Federal and State of Connecticut personal income taxes
of approximately $.029 per share were paid to shareholders.* Reinvesting
these dividends and calculating the effect of compounding resulted in an
annualized effective yield of 2.93%.**
    Data over the past few months have largely continued to show a strong
U.S. economy, although there were some signs of softening as September drew
to a close. Real Gross Domestic Product (GDP) rose 2.1% in the first quarter
of 1996, 4.8% in the second. Housing sales remained relatively robust, and
consumer confidence was high. The big news came on the job front in August,
as hourly wages rose by six cents and unemployment dropped to 5.1%, a new low
for this business cycle. Signs of a slowdown began to appear in the September
job data, which indicated mild declines in nonfarm and manufacturing
payrolls, along with modest gains in private sector employment. Summer retail
sales figures were also somewhat sluggish, new factory orders dropped in
August, and the widely watched purchasing managers' Index showed a
deceleration in factory activity.
    Nonetheless, it was far from certain that the economy was retrenching.
Once again, inconclusive economic evidence - and conflicting statements from
Federal Reserve Board (the "Fed") officials - gave rise to the market's
favorite pastime: guessing what the Fed would do with short-term interest
rates at its next meeting. Many, if not most, market participants believed
the Fed would raise rates slightly, perhaps by 1\2 or 1\4 percentage point.
In fact, the Fed left the Fed Funds rate unchanged, believing the economy
would soon slow enough to dampen any inflationary forces that might be
building.
    In the money market nationwide, expectations for a Fed interest-rate hike
led to somewhat higher yields throughout most of the period. Yields had
already been inching up since March, when the first robust employment growth
figures of 1996 were announced. More specifically, Connecticut's economy
appears to be speeding up in the second half of 1996 even as the national
economy shows signs of slowing. Connecticut continues a trend of steady
employment growth. The unemployment rate remains 4.8%, well below the
national figure. Boosted by an improving economy and sharp spending cuts, the
State finished the past fiscal year with a surplus of $250 million - the
highest in the past nine years. At the same time that costs were being cut,
the State's economy has been steadily improving from the sharp downturn of
the early 1990s.
MARKET ENVIRONMENT/PORTFOLIO ACTIVITY
    If one were to trace the trend in short-term municipal rates over this
most recent six-month period, the direction would mirror closely the changes
in supply and demand conditions. The six-month cycle reflected: price
weakness and higher rates in April as investors tapped their money market
funds to pay income taxes; market strength in late June and early July as $9
billion in maturing notes left the market; and price weakness and buying
opportunities in late July due to inflationary concerns and the added supply
of summer financings. These technical influences continue to be the
overriding factor affecting municipal money rates.

    These conditions, coupled with Fed policies, provide the framework for
our investment strategy-both on a day-to-day basis and looking ahead over a
one-year horizon. In late April, the short-term market exhibited signs of
weakness as a result of redemptions due to tax payments. While this
supply/demand imbalance was only temporary, it translated, for a time, into
higher yields on short-term securities. During this period, the purchase of
attractively yielding Connecticut-exempt commercial paper in the 60- to
90-day range allowed us to capture returns similar to those on one-year
issues.
    The opportunity for the market to commit to the longer note issues
appeared in July and August. We did, to some extent, participate in these
offerings, which resulted in an extension of your Fund's average maturity to
the 60-day range. We will take advantage of any additional buying
opportunities that represent an attractive return as we monitor potential Fed
activity and any other significant changes in the municipal market. All new
investments will continue to meet the high credit quality standards which we
require and to provide a significant level of liquidity, commensurate with
the needs of your Fund.
    Included in this report is a series of detailed statements about your
Fund's holdings and its financial condition. We hope they are informative.
Please know that we appreciate greatly your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Very truly yours,

                          [Richard J. Moynihan signature logo]

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
October 15, 1996
New York, N.Y.

*  Some income may be subject to the Federal Alternative Minimum Tax (AMT)
for certain shareholders.
**Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
<TABLE>
<CAPTION>


DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                             SEPTEMBER 30, 1996
                                                                                                      PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                           AMOUNT        VALUE
                                                                                                        _______      _______
<S>                                                                                                 <C>          <C>
CONNECTICUT-96.2%
Town of Cheshire, BAN 4.25%, 8/8/97.........................................                        $ 2,625,000  $ 2,634,689
State of Connecticut:
    Economic Recovery Notes, Refunding 4.25%, 12/15/96......................                          5,000,000    5,005,463
    Special Tax Obligation Revenue, VRDN (Transportation Infrastructure-1)
      3.80% (LOC; Commerzbank) (a,b)........................................                          9,000,000    9,000,000
Connecticut Development Authority, VRDN:
    Health Care Revenue (Corp. for Independent Living Project)
      3.70% (LOC; Chase Manhattan Bank) (a,b)...............................                         14,245,000   14,245,000
    IDR (Blaset and Bromley Realty Project) 3.90% (LOC; Fleet Bank) (a,b)...                          3,560,000    3,560,000
    PCR:
      (Connecticut Light and Power Co. Project):
          3.85%, Series A (LOC; Canadian Imperial Bank of Commerce) (a,b)...                         17,200,000   17,200,000
          Refunding:
            3.85%, Series B (LOC; Union Bank of Switzerland) (a,b)..........                          9,000,000    9,000,000
            3.90%, Series A (LOC; Deutsche Bank) (a,b)......................                         18,500,000   18,500,000
      (Western Massachusetts Electric Co.)
          3.75%, Series A (LOC; Union Bank of Switzerland) (a,b)............                          8,800,000    8,800,000
    Solid Waste Revenue (Rand/Whitney Project)
      3.65% (LOC; Chase Manhattan Bank) (a,b)...............................                          5,500,000    5,500,000
Connecticut Health and Educational Facilities Authority, Revenue:
    CP (Windham Community Memorial Hospital)
      3.55%, 10/22/96 (LOC; Banque Paribas) (b).............................                          9,250,000    9,250,000
    VRDN (Charlotte Hungerford Hospital)
      3.65%, Series B (LOC; Bank of Boston) (a,b)...........................                            900,000      900,000
Connecticut Housing Finance Authority (Housing Mortgage Finance Program):
    CP 3.60%, Series D, 11/12/96............................................                          3,445,000    3,445,000
    Revenue 3.65%, Subseries A-4, 4/10/97...................................                          5,200,000    5,200,000
    VRDN 3.75%, Series G (BPA; Morgan Guaranty Trust Co. and Insured; AMBAC) (a)                      9,365,000    9,365,000
Connecticut Municipal Electric Energy Co-op, Power Supply System Revenue:
    CP 3.50%, Series A, 12/11/96 (LOC; Fleet Bank) (b)......................                          3,600,000    3,600,000
    Refunding 4%, 1/1/97 (Insured; MBIA)....................................                            700,000      701,250
Connecticut Special Assessment Unemployment Compensation Advance Fund,
Revenue
    (Connecticut Unemployment)
    3.90%, Series C, 7/1/97 (Insured and Liquidity; FGIC)...................                         15,000,000   15,000,000
Hartford Redevelopment Agency, MFMR, Refunding, VRDN
    (Underwood Tower Housing Project)
    3.75% (Insured; FSA and Liquidity; Barclays Bank) (a)...................                          9,000,000    9,000,000
Town of Meriden, BAN 4.25%, 8/13/97.........................................                          6,875,000    6,896,725
Town of Milford, BAN 4.10%, 11/14/96........................................                          6,475,000    6,478,224
City of New Haven, BAN 3.95%, 5/22/97 (LOC; Fleet Bank) (b).................                          7,475,000    7,487,759

DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                     SEPTEMBER 30, 1996
                                                                                                       PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                      AMOUNT        VALUE
                                                                                                        _______      _______
CONNECTICUT (CONTINUED)
Stamford Housing Authority, Revenue, VRDN (Morgan Street Project)
    3.85% (LOC; Deutsche Bank) (a,b)........................................                          7,500,000  $ 7,500,000
U.S. RELATED-3.8%
Commonwealth of Puerto Rico Government Development Bank, CP:
    3.55%, 10/9/96..........................................................                          4,000,000    4,000,000
    3.50%, 10/10/96.........................................................                          3,000,000    3,000,000
                                                                                                                     ______
TOTAL INVESTMENTS (cost $185,269,110).......................................                                    $185,269,110
                                                                                                                    ========
</TABLE>
<TABLE>
<CAPTION>


SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <S>     <C>
AMBAC         American Municipal Bond Assurance Corporation      LOC     Letter of Credit
BAN           Bond Anticipation Notes                            MBIA    Municipal Bond Investors Assurance
BPA           Bond Purchase Agreement                                         Insurance Association
CP            Commercial Paper                                   MFMR    Multi-Family Mortgage Revenue
FGIC          Financial Guaranty Insurance Company               PCR     Pollution Control Revenue
FSA           Financial Security Assurance                       VRDN    Variable Rate Demand Notes
IDR           Industrial Development Revenue
</TABLE>

<TABLE>
<CAPTION>


SUMMARY OF COMBINED RATINGS (UNAUDITED)
MOODY'S                             OR                STANDARD & POOR'S                         PERCENTAGE OF VALUE
____                                                 __________                                  ___________
<S>                                                   <C>                                           <C>
VMIG1/MIG1, P1 (c)                                    SP1+/SP1, A1+/A1 (c)                          84.3%
Aaa/Aa (d)                                            AAA/AA (d)                                     6.8
Not Rated (e)                                         Not Rated (e)                                  8.9
                                                                                                   ____
                                                                                                   100.0%
                                                                                                   ====
</TABLE>

NOTES TO STATEMENT OF INVESTMENTS:
    (a)Securities payable on demand. The interest rate, which is subject to
    change, is based upon bank prime rates or an index of market interest
    rates.
    (b)Secured by letters of credit. At September 30, 1996, 60.3% of the
    Fund's net assets are backed by letters of credit issued by domestic
    banks and foreign banks, of which Deutsche Bank and Chase Manhattan Bank
    provided letters of credit to 13.7% and 10.4%, respectively, of the
    Fund's net assets.
    (c)  P1 and A1 are the highest ratings assigned tax-exempt commercial
    paper by Moody's and Standard & Poor's, respectively.
    (d)                                        Notes which are not MIG or SP
    rated are represented by bond ratings of the issuers.
    (e)Securities which, while not rated by Moody's and Standard & Poor's,
    respectively, have been determined by the Fund's Board of Directors to be
    of comparable quality to those rated securities in which the Fund may
    invest.

See notes to financial statements.
<TABLE>
<CAPTION>


DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                   SEPTEMBER 30, 1996
<S>                                                                                                     <C>     <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                    $185,269,110
    Cash....................................................................                                       3,780,710
    Interest receivable.....................................................                                       1,113,198
                                                                                                                     ------
                                                                                                                 190,163,018
LIABILITIES:
    Due to The Dreyfus Corporation and affiliates...........................                            $83,557
    Accrued expenses and other liabilities..................................                             52,075      135,632
                                                                                                         ------      -------
NET ASSETS  ................................................................                                    $190,027,386
                                                                                                                     =======
REPRESENTED BY:
    Paid-in capital.........................................................                                    $190,105,942
    Accumulated net realized (loss) on investments..........................                                         (78,556)
                                                                                                                     -------
NET ASSETS at value applicable to 190,105,942 shares outstanding
    (1 billion shares of $.001 par value Common Stock authorized)...........                                    $190,027,386
                                                                                                                     =======
NET ASSET VALUE, offering and redemption price per share
    ($190,027,386 / 190,105,942 shares).....................................                                           $1.00
                                                                                                                     =======








See notes to financial statements.

DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                                     YEAR ENDED SEPTEMBER 30, 1996
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                      $7,564,670
    EXPENSES:
      Management fee-Note 2(a)..............................................                         $1,067,581
      Shareholder servicing costs-Note 2(b).................................                            267,847
      Professional fees.....................................................                             41,266
      Custodian fees........................................................                             22,639
      Directors' fees and expenses-Note 2(c)................................                              8,900
      Prospectus and shareholders' reports..................................                              4,967
      Registration fees.....................................................                              1,426
      Miscellaneous.........................................................                              9,439
                                                                                                          _____
          TOTAL EXPENSES....................................................                          1,424,065
      Less-reduction in management fee due to undertaking-Note 2(a) ........                             67,375
                                                                                                          _____
          NET EXPENSES......................................................                                       1,356,690
                                                                                                                       _____
INVESTMENT INCOME-NET, representing net increase in net assets
    resulting from operations...............................................                                      $6,207,980
                                                                                                                       =====



See notes to financial statements.

DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                                  YEAR ENDED SEPTEMBER 30,
                                                                                           ----------------------------------
                                                                                               1995                     1996
                                                                                              _______                  ______
OPERATIONS:
    Investment income-net...................................................         $     8,278,417          $     6,207,980
    Net realized (loss) on investments......................................                 (33,920)                  --
                                                                                              _______                  ______
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS..................               8,244,497                6,207,980
                                                                                              _______                  ______
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net...................................................              (8,278,417)              (6,207,980)
                                                                                              _______                  ______
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold...........................................             357,211,843              304,245,758
    Dividends reinvested....................................................               7,853,761                5,969,752
    Cost of shares redeemed.................................................            (374,167,329)            (353,119,723)
                                                                                              _______                  ______
      (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS..............              (9,101,725)             (42,904,213)
                                                                                              _______                  ______
          TOTAL (DECREASE) IN NET ASSETS....................................              (9,135,645)             (42,904,213)
NET ASSETS:
    Beginning of year.......................................................             242,067,244              232,931,599
                                                                                              _______                  ______
    End of year.............................................................           $ 232,931,599            $ 190,027,386
                                                                                              =======                  ======

</TABLE>

See notes to financial statements.


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 year indicated. This information
has been derived from the Fund's financial statements.
<TABLE>
<CAPTION>



                                                                                YEAR ENDED SEPTEMBER 30,
                                                              -----------------------------------------------------------
PER SHARE DATA:                                                  1992        1993        1994        1995        1996
                                                                 ----        ----        ----        ----        ----
    <S>                                                      <C>         <C>         <C>         <C>         <C>
    Net asset value, beginning of year...........            $   1.00    $   1.00    $   1.00    $   1.00    $   1.00
                                                                 ----        ----        ----        ----        ----
    INVESTMENT OPERATIONS;
    Investment income-net........................                .032        .023        .023        .033        .029
                                                                 ----        ----        ----        ----        ----
    DISTRIBUTIONS;
    Dividends from investment income-net.........               (.032)      (.023)      (.023)      (.033)      (.029)
                                                                 ----        ----        ----        ----        ----
    Net asset value, end of year.................            $   1.00    $   1.00    $   1.00    $   1.00    $   1.00
                                                                 ====        ====        ====        ====        ====
TOTAL INVESTMENT RETURN..........................                3.28%       2.34%       2.33%       3.35%       2.94%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......                 .04%        .12%        .22%        .45%        .63%
    Ratio of net investment income to average net assets         3.22%       2.30%       2.30%       3.31%       2.90%
    Decrease reflected in above expense ratios due to
      undertakings by the Manager................                 .63%        .55%        .42%        .18%        .03%
    Net Assets, end of year (000's Omitted)......            $206,980    $212,288    $242,067    $232,932    $190,027
</TABLE>



See notes to financial statements.

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 ("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 ("Manager") serves as the Fund's investment adviser. The
Manager is a direct subsidiary of Mellon Bank, N.A. Premier Mutual Fund
Services, Inc. acts as 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 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.
    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, if any, 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. 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 Internal
Revenue 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 $79,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to September 30, 1996. If not
applied, $34,000 of the carryover expires in fiscal 2002, $11,000 of the
carryover expires in fiscal 2003, and $34,000 of the carryover expires in
fiscal 2004.

DREYFUS CONNECTICUT MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    At September 30, 1996, 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).
NOTE 2-MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("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 Agreement
provides that if in any full fiscal year the aggregate expenses of the Fund,
exclusive of taxes, brokerage, interest on borrowings and extraordinary
expenses, exceed the expense limitation of any state having jurisdiction over
the Fund, the Fund may deduct from payments to be made to the Manager or the
Manager will bear the amount of such excess to the extent required by state
law. The Manager has undertaken from October 1, 1995 through September 30,
1997, to reduce the management fee paid by, or reimburse such excess expenses
of the Fund, to the extent that the Fund's aggregate annual expenses
(exclusive of certain expenses as described above) exceed 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 $67,375 during
the year ended September 30, 1996.
    The undertaking may be extended, modified or terminated by the Manager,
provided that the resulting expense reimbursement would not be less than the
amount required pursuant to the Agreement.
    (B) Pursuant to the Fund's 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 year ended September 30, 1996, the Fund was charged an aggregate
of $160,861 pursuant to the Shareholder Services Plan.
    Effective December 1, 1995, 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. Such compensation amounted to $56,739 during the period ended
September 30, 1996.
    (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, 1996, 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. Our procedures included confirmation of
securities owned as of September 30, 1996 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, 1996, 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.

                              [Ernst and Young LLP signature logo]
New York, New York
October 30, 1996




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, 1996 as "exempt-interest dividends" (not subject to regular
Federal and, for individuals who are Connecticut residents, Connecticut
personal income taxes).


[Dreyfus lion "d" logo]
Connecticut
Municipal
Money Market
Fund, Inc.
Annual Report
September 30, 1996
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.                            101AR969
[Dreyfus logo]



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