Quote Quoting llworking
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I don't see how the retail establishment could obtain the credit card records of the alleged thief. Based on the question asked, those records would be the necessary first step in doing the described investigating.
Given the wording of the OP, I took it to mean for a particular store/chain. If so, no they do not need the records. Depending on what system they are using, all they need is a name or be able to identify a transaction where OP used their CC (so they can obtain the last 4 digits) and they can run them down that way. There are of course some limitations to that method, mostly the time involved so unless they believe OP is a serial thief (sounds like maybe they are ticket switching or engaging in return fraud) the retailer is not likely to go to a lot of effort.