November 1, 2004

DREYFUS PREMIER STATE MUNICIPAL BOND FUND 

SUPPLEMENT TO STATEMENT OF ADDITIONAL INFORMATION 

DATED AUGUST 31, 2004

The following information replaces all contrary information contained in the section of the Statement of Additional Information ("SAI") entitled "How to Buy Shares - Dreyfus TeleTransfer Privilege":

Dreyfus TeleTransfer Privilege. You may purchase shares by telephone or online if you have checked the appropriate box and supplied the necessary information on the Account Application or have filed a Shareholder Services Form with the Transfer Agent. The proceeds will be transferred between the bank account designated in one of these documents and your Fund account. Only a bank account maintained in a domestic financial institution which is an Automated Clearing House (“ACH”) member may be so designated.

Dreyfus TeleTransfer purchase orders may be made at any time. If purchase orders are received by 4:00 p.m., Eastern time, on any day that the Transfer Agent and the New York Stock Exchange (“NYSE”) are open for regular business, Fund shares will be purchased at the public offering price determined on that day. If purchase orders are made after 4:00 p.m., Eastern time, on any day the Transfer Agent and the NYSE are open for regular business, or made on Saturday, Sunday or any Fund holiday (e.g., when the NYSE is not open for business), Fund shares will be purchased at the public offering price determined on the next bank business day following such purchase order. To qualify to use the Dreyfus TeleTransfer Privilege, the initial payment for purchase of shares must be drawn on, and redemption proceeds paid to, the same bank and account as are designated on the Account Application or Shareholder Services Form on file. If the proceeds of a particular redemption are to be sent to an account at any other bank, the request must be in writing and signature-guaranteed. See “How to Redeem Shares--Dreyfus TeleTransfer Privilege.”