This is a check, and there's no required investigation steps like those involved with a claim that an EFT was not authorized. There is also no requirement that you credit the customer if you believe the customer's affidavit is fraudulent (or, to put it less judgmentally, you believe the customer is mistaken). The Uniform Commercial Code basically says that, given a set of established facts, there is a prescribed outcome. So far, you don't have facts; you have an allegation from the customer. You can require the customer to file a police report (remember, this isn't Regulation E territory). You can also inform your customer that, if the affidavit it proven to be fraudulent, there could be legal consequences for him or her.
Consult with your bank's attorney, making sure you tell him or her that you believe the affidavit is false.
An afterthought: You indicated that the check was cashed at the bank. I presume you have surveillance film that could show who cashed the check. It would be interesting to know who that is, and what his/her relationship is to your customer.