Are banks required to have a branch closing policy and will the regulators cite violations for not having one? Thanks.

Yes, you are required to have a policy -- click here for 12 USC 1831r-1(c)

(c) ADOPTION OF POLICIES.--Each insured depository institution shall adopt policies for closings of branches of the institution.

or here's the OCC licensing manual

Yes banks are required to have a policy even if you have never closed or relocated a branch. When I first started with the bank (15 years ago) we didn't have one and the examiners (OTS) told us we needed one. They didn't write us up for not having one.