I had to figure all this out after the fact, by the way - the movie clearly expected the audience would be familiar with the radio show and format.
At any rate, the movie starts with a bunch of guys sitting around a newspaper office at night, playing cards, until one starts telling the story. And it isn't much of a story.
A police detective, while in the midst of meeting his mistress, witnesses a crime. He can't report it because he's cheating on his wife and can't explain why he was in the area to witness it without outing himself, but his mistress--also married, and very wealthy and some sort of society dame, to boot--also can't report it for similar reasons. So the cop goes through the motions of investigating the crime, without being able to simply go to the crook who committed it and arrest him. This leads to further troubles when the investigation points towards a man the detective knows is innocent, so of course, he's conflicted and faces moral dillemas, let's say.
All in all, it was a sorry effort of a film. Its best quality is it's barely an hour. I suppose it was intended to start of a series of these, making the transition from radio to film, but that never happened. And if this is the foot they chose to start off on, it's probably for the best.