Is there any requirement to notify safe deposit box owners when moving them into a new bank building?

I can't point you to any specific regulation, but I used to work for a bank that participated in several moves of Safe Deposit Boxes and depending on the distance, we gave the customer 30, 60 or 90 days notice. Maybe you should check with specific rules of the state that you live.

In my experience, this is included in the safe deposit contract.

Certainly from a customer service issue they should be notified. You may cross reference safe deposit customers against banking customers and see which may be unique and do a targeted mailing to just this group as the others will receive separate notices if this is a branch closing.

I agree with Andy that notifying the customer makes good sense from a customer service standpoint. However, you may also want to search your State Law for any specific requirements. If you are located in Texas, the Finance Code requires that we mail to the lessee a notice of relocation 30 days prior to a non-emergency move. The notice must state the scheduled date and time of the relocation and whether the box will be opened during the relocation. A lessee should be given the opportunity to personally supervise the relocation or authorize the relocation in writing.