A Dangerous Game (1941)

Detectives Dick Williams and Andy McAllister find themselves trying to solve several crimes at an isolated mentally-ill hospital, where the patients range from slightly daffy to criminally insane, and they don't know which is which. A gang is out to steal a fortune inherited by one of the patients and, before Dick and Andy solve the case, several patients are transferred to the cemetery. And 'tiddlie-winks" are indeed involved.