Answer:
The customer should receive a copy of the account agreement. If the customer is a consumer, he or she must receive the disclosures required by TISA and CFPB Regulation DD, in a form that can be kept. As for the signature card, there's no reason to provide a copy unless it includes information that the customer ought to have. Since the layout, format and content of signature cards varies widely between institutions, I have to suggest that you review your institution's signature card to see what's there and decide if the customer ought to have a copy.