The proposed regulation just deals with account opening and really only addresses signatories on the account.
Although not required under the proposed regulation, anyone conducting business in your bank should probably be subject to some type of identity verification just as a matter of prudent business practice. The regulations also do not require identity verification of non-customers cashing checks in your bank either - but I bet you have a procedure in place to do that very thing if you cash checks for non-customers.
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Jim Bedsole, CRCM, CBA, CFSA, CAFP
My posts - my opinions