The bank can chose to honor a stop payment request on a certified check. The bank may be liable for damages relating to a wrongful dishonor if it chooses to enforce the stop payment request.
For a certified check, the bank verifies that the signature on the check is genuine and that there are enough funds in the account to cover the total amount of the check. Both the bank and the customer sign the check. In addition to the bank, the customer is also liable if there is something wrong with the certified check. The bank may occasionally impose time restrictions on cashing the certified check.