A gang of criminals, which includes a piano player and an imposing former convict known as 'Gruesome', has found out about a scientist's secret formula for a gas that temporarily paralyzes anyone who breathes it. When Gruesome accidentally inhales some of the gas and passes out, the police think he is dead and take him to the morgue, where he later revives and escapes. This puzzling incident attracts the interest of Dick Tracy, and when the criminals later use the gas to rob a bank, Tracy realizes that he must devote his entire attention to stopping them.
Bill Kirby, a dandy living off his aunt, wishes her dead in public and catches the ear of Radek, a desperate fellow who is very clever but also a bit loopy. Radek offers to murder the old lady so Kirby can get his inheritance, pay off his wife to divorce him, and marry his wife's friend. On the night of the murder, a would-be burglar named Heurtin stumbles upon the corpses of the old lady and her maid. Heurtin, who is almost legally blind, loses his glasses and must be helped home by the killer. Inspector Maigret is assigned to the case and quickly tracks down the owner of the thick glasses. Heurtin helps identify the Radek, but there is no real evidence against him. So begins a clever game of cat-and-mouse, in which Radek taunts the police with clues and his dirty money and blackmails
The shriek of the title is uttered by a millionaire when he plummets to his death from his penthouse balcony.
Ginger Rogers and Lyle Talbot are rival newspaper reporters always trying to outscoop each other. They join together to solve a series of murders being committed in an apartment building.