Are banks legally required to perform criminal background checks on new employees?

There is no regulatory requirement to perform a criminal background check. However, you need to read your bonding insurance policy for any requirements they may impose for checking on new hires.

You should, however, be familiar with the FDIC requirements regarding individuals who have been convicted of certain crimes becoming "institution affiliated parties".

FDIC requirements

In a previous position, the OCC has previously relied on that FDIC provision to require a national bank to background check every employee- call center employees, etc.

See FIL 46-2005 http://www.fdic.gov/news/news/financial/2005/fil4605.pdf