ABE books, the online used and rare books vendor, is featuring a page on locked room mysteries. Among those listed are Clayton Rawson's Death From a Top Hat, which features Rawson's conjuror sleuth The Great Merlini, and Hake Talbot's The Rim of the Pit (1944). Hake Talbot is better known as Henning Nelms, stage magician and attorney. Nelms also wrote another mystery, The Hangman's Handyman (1942), and two short stories, The High House and The Other Side. All his works feature the sleuth Rogan Kincaid.
Clayton Rawson, a stage magician who like Henning Nelms who wrote several books on magic, wrote four Merlini novels: Death From a Top Hat (1938) The Footprints on the Ceiling (1939), The Headless Lady (1940) and No Coffin For the Corpse (1942). Robert Young (who later starred in the TV series Father Knows Best) starred in an adaptation of Death From a Top Hat as The Great Morgan in the film Miracles For Sale in 1939. In 1942 Lloyd Nolan, the noted actor, was featured in an adaptation of No Coffin For the Corpse called The Man Who Wouldn't Die.
The magician, either as sleuth or as perpetrator, is a natural for the locked room mystery, of course. More locked room mysteries are as near as the bookshelf or film and tv library. Try Otto Penzler's collection, Whodunit? Houdini? Thirteen Tales of Magic, Murder, Mystery (Harper & Row, 1976) and the television series Jonathan Creek. And check out this wonderful Genii forum thread on magic and magician-themed mysteries.