Although Philip Ober is credited as playing only Sumner Hodge, he also plays Sumner's brother, Adrian, using a hairpiece and glasses.
It's possible the plot of this episode was inspired by the much-publicized 1909 murder of George Harry Storrs. Like Sumner Hodge, Mr. Storrs engineered a phony murder attempt on himself to arouse the attention of police, and was really murdered sometime later.
Other episodes in the series where an actor played dual roles were The Case of the Pathetic Patient (1961) (Frank Cady) and The Case of the Dead Ringer (1966) (Raymond Burr). The Case of the Duplicate Daughter (1961) involves twins but one is never seen, either in person or in a photograph.
The song Con is playing in the club when first introduced is the same song Stephen Bishop is playing on the stairway at the Delta Toga Party in National Lampoon's Animal House (1978). The song causes Bluto (John Belushi) to go berserk and smash the guitar. It's a traditional song often given the title "The Riddle Song" or "I Gave My love A Cherry".
The song "This Train is Bound for Glory" was also used in "The Case of the Bogus Books" where it is sung by Adam West.