How DOooo You Do (1945) 

This film is covered on THE FORGOTTEN HORRORS PODCAST.
Two radio comics go to Desert Springs, one to get away from his jealous wife and the other to escape the attentions of a comedienne. The body of an agent is found in their room and later disappears. After some sleuthing by the actors and some other detectives, changed just enough from well-known fiction-and-movie detectives to keep from being sued, it is discovered that the agent was not killed, but his body had been concealed by his doctor, who had been experimenting with a new cure for heart trouble...none too well evidently.