I Wouldn't be in your Shoes [1948] [DVD]

Tom (Don Castle) and Ann (Elyse Knox) are a down-and-out dance team, and while Don seeks engagements, Ann works as an instructor at a dance academy, with Detective Judd (Regis Toomey) one of the many customers she meets. On a hot summer night Tom, awaken from his sleep, tosses his only pair of shoes out the window to quiet two noisy cats. He goes down to retrieve them and can't find them, but Ann discovers them in front of their door the next morning. A near-by recluse is found murdered in his old shack that same day while Tom finds a wallet filled with old $20 bills. Footprints, bearing an imprint like those on a tap-dancer's shoes, plus Don's new-found wealth combine to make a good circumstantial evidence case for Judd against Tom and he is convicted. On the night before his execution, Ann seeks Judd's help in proving Tom is innocent. He turns up a suspect, Kosloff (Robert Lowell), but an air-tight alibi clears him.

Here is a review from imdb:

A dancer chucks his tap shoes out the window at a noisy cat and ends up facing a murder charge. I could make a comparison to a certain other film noir (actually a film noir and its remake) but that would be giving away its surprising twist. Given the era, you know the innocent man will get a last minute reprieve, the trick is how we get to that point. When the realization dawned on me -- about 30 seconds before the first real clue -- it was one of those magic "How did I not see this coming?" moments. Certain plot points that at first seemed very contrived clicked into place (although to be totally honest, a lot of it is still kinda contrived... goofy coincidences and twists are something of a trademark for Cornell Woolrich). The film is clearly a shoestring budget production, but even if the performances aren't great, they are at least sincere. The "wrong man" scenario provides the usual (justified) paranoia concerning the authorities charged with protecting us, and the tight running time makes this a worthwhile picture, even if not exactly an undiscovered classic.