Amy, Andy is right on the State law issue. Since you are in New York Article VIII-A, Section 335 (Safe Deposit Business) of the New York Banking law applies. Yes, it requires that a notary along with an officer/or employee designated by the bank be present when a box is broken open. The certificate listing the contents (if any) must be notarized. There is no requirement to use an outside notary. Whether to use an outside notary or a bank notary differs among New York State Safe Deposit Association member banks here in New York City. Some use an outside notary, some use a vault attendant who is also a notary, and others use a bank notary that is not associated with the vault when doing break opens.
Here's the link to the NY State law if you don't already have it: http://assembly.state.ny.us/cgi-bin/claws?law=9&art=22
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