A pretty decent police procedural. A better title could have been CSI:1950 Boston; because it's never quite clear where Mystery Street is located (between Mt. Vernon and Pinckney, maybe?)
As the movie begins, we follow Vivian, a Scolloy Square, um, performer, as she hassles an unseen paramour on the Cape. She dupes Henry, who's depressed and drunk, into letting her drive his car to Hyannis. Once there, she gives Henry the slip to meet her lover, but things don't work out as she expects. And, months later, a beachcomber comes across her skeleton.
This brings in the cops, primarily Pete Moralas, played by Ricardo Montalban! ("Khaaaaan!") He gets help from Harvard Med School guys to analyze Vivian's remains, and his diligent police work soon turns up… Henry, the wrong guy. Meanwhile, Mrs. Smerrling (Elsa Lanchester! Hissss!), Vivian's ditzy but avaricious landlady, has inside information she's not telling Pete.
This movie was, in fact, the first commercial movie mostly shot in the Boston area. ("Ah, so that's what Harvard Square looked like back then.") The climax takes place at "Trinity Station", which got wiped out by the Mass Pike, near the current Back Bay Amtrak/MBTA station.