Is anyone aware of any code that limits how close a gas pipe may be to an electrical panel assuming that all working clearance requirements of NEC 110 are met? (It's in a hospital boiler room.)

You would have to know what gas code is adopted in your area. If it is the International Fuel Gas Code (IFGC), it is not addressed. If it is the NFPA 54, I'm not sure, as I have never read that document.

Check with your local utilities as well - I know out PoCo (ComEd) lists a zone around the meter for gasworks in their handbook...

NFPA 54 (Fuel Gas Code) Section 2.7.2(c)
requires that gas meters be located 3' from sources of ignition. Our PoCo requires electric meters be 3' away from gas meters.
But, I don't think that gas piping is an issue as long as the clearances from the electrical panel are observed.

Ok, thanks for your help!