Randy Carey
If you are referring to your customer's signature on the check as the drawer, you have until your midnight deadline.
John Burnett
The basis for the answer to your question was established in a famous court case in England in the 1700s (Price vs. Neal) that established that a bank is responsible for having paid a draft bearing the forged signature of its customer. Bringing that court decision into today's context, the Uniform Commercial Code as adopted in all U.S. states provides that a paying bank that fails to return a forged check or a notice in lieu of the check by its midnight deadline (midnight of the banking day following the banking day the check was presented for payment) is responsible for the amount of the check.
To put it simply, when it was established that your bank had, in fact, paid a forged check against the account of its customer, the bank became liable to its depositor for the amount of the check, and had no recourse against the depositary bank or any other bank that handled the check. It's only recourse is against the forger, if the forger can be identified and prosecuted.
The results of applying the UCC can be modified by agreement between the parties. Some check clearing house associations have adopted a warranty provision as part of their membership agreements such that a depositary bank member of the association warrants to the paying bank that the drawer's signature is not forged and/or the check is not counterfeit. For more discussion on this so-called "Rule 9" warranty, see this earlier Q&A .
If your bank has not yet made its depositor whole for the amount of the forged check, there could be situations in which the bank would have a defense against the depositor's claim of wrongful payment. Examples include ratification of previous forgeries by the same individual; delayed notice in the case of multiple forgeries by the same wrongdoer; the depositor's acceptance of a benefit resulting from the forgery; the depositor's negligence contributing to or facilitating the forgery, etc. There's a very helpful discussion of these defenses and other aspects of liability for forged or counterfeit checks beginning on page 1 of The Check Book, by Gene Elerding, available as a free PDF download from BOL's Banker Tools pages.