Odd Man Out was generally released on 17 March 1947, St Patrick's Day. A week earlier Sidney Gilliat's Green for Danger went the rounds with another score by Alwyn. The film was well received, although later Gilliat wrote that “it mortified me somewhat that nobody at all spotted that it was, so to speak, a film presented in quotation marks, dotted with stereotypes of half a century of detective fiction, with an affectionate side-swipe at the arrogantly omniscient Detective figure of the genre”. If the critics had paid more attention to the musical clues, they might have picked up on Gilliat's stratagem.

The plot, based on a Christianna Brand detective yarn, is set in a temporary wartime hospital during the days of the V-1 bomb. The narrator is Inspector Cockrill (Alastair Sim), a conceited, sadistic buffoon called in to investigate two murders, the first a patient under anaesthetic, the second a stabbed nurse. Mood is established by Alwyn's title music, an exhilarating fugue, but lacking the determined menace of a thriller. Gilliat explained how it came to be written:

There is an even stronger early clue to the film's idiom. A pan around an operating table pauses on each of the five doctor and nurse suspects. Alwyn matches each camera movement with a short scale, interrupted by plucked strings - a semi-humorous, mocking effect. In a later scene the plucked strings are replaced by a celesta, which is funnier. Indeed, as the plot advances the music takes on an increasingly mocking tone. A descending discordant, scratchy violin phrase marks the chalking of the first fatal operation schedule on a blackboard : a warning. When the second operation is chalked up, the scratchier repeat of the phrase is flippant.