Signiture

My wife left several months back. She is a authorized user on my credit, I should say was a authorized user, I had her dropped off the card. And got a new credit card number. She apparently took some credit card checks, with my name only on them. She tried or did pass a $300.00 check............I received notification from the credit card company, that they declined paying it. It was declined because the card was reported lost. Now, question is this, would she have to sign my name to the check, or because she was a authorized user sign her name, even tho my name only appears on the check. (She must have thought the old card was still good)
I called the company, and they were of no help, they don't know who signed it, and can't tell me the answer to the question I am asking in this forum. I requested a copy of the check, and they said it was returned to the merchant.

Thanks