Brain Twister - by Gordon Randall Garrett and Laurence Mark Janifer

An FBI agent's work is never easy.

note:  this is a very funny little story from 1962, set a decade in the future, and uses non-PC terminology (a lot) to refer to all aspects of psychiatry, including patients.  If you are easily offended by terms like "imbecile", "nuthouse", and "loon", in a historic and comic context, this is probably not the story for you.