I have to agree with the above comments, that a customer should at least be given the opportunity to have a copy when they sign. However, requesting a copy at a later time is a little different. The signature card is most definately non-public information, and could be quite useful in conducting ID theft. Some diligence in being sure you are dealing with the account holder(s) might be a good idea before simply making a copy and giving it to anyone who asks.
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Everyone has to make a living, mine just happens to involve thumbscrews.