In a recent HAZOP, operators told me that they were under the impression that we could not install a check valve on a PSV discharge.  Can anybody point me to the code that would reference this?

API RP 520 paragraph 9.3 may address the issue.  Some of the installation guidelines related to back pressure address the issue but without mentioning a check valve per se.

A PSV >IS< a check valve...spring-loaded closed.  Aside from the code issues that JLSeagull mentioned, it's just unnecessary.  Anything that comes backward in the line should go to a drain. 

Nothing should backflow thru a PSV; it is a check valve.

Besides, I can not think why you might want to place any restrictive device, or a device subject to mechanical failure downstream.