We recently had a situation at our ATM which involved the potential unauthorized use of a customer's debit card. When the local police were notified, they requested the security tape to observe the pictures taken by the ATM camera of the possible suspect. Under the circumstances would this raise any Privacy issues since obviously there are other customers on the tape?

I wouldn't think so - how would the police know if they are your customer's or customer's of another financial institution?

How it works at our bank is we make a copy just of the transaction that is in question and give it to the cops.

You should develop an evidence policy to fall back upon that indicates how your institution will comply with an agency's requests for information -- and this is a great example. Remember that the Bank Protection Act requires that every institution must "assist in the identification, apprehension and prosecution of offenders". Law enforcement agencies are very aware of an institution's privacy requirements (in most cases) and the agency may obtain a subpoena or a search warrant (jurisdictions vary on how this is to be done) for information relating to a specific transaction. Contact your local prosecuting attorney for more information and loop your institution's legal counsel into the process before you produce the images and related records.