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While flying to Santa Catalina Island, schoolteacher and amateur detective Hildegarde Withers witnesses the sudden death of fellow passenger Roswell T. Forrest. Although Britt, the Catalina police chief, insists that Forrest died of a heart attack, Hildegarde is confident that Forrest was murdered and wires her friend, Inspector Oscar Piper, in New York City. There, Oscar learns that Forrest was to be a state's witness against a gang of mobsters, and that a mobster named McArthur was offering $10,000 for Forrest's death. Convinced now that Forrest was murdered, Britt begins to question the plane passengers, which include Joseph B. Tate, a motion picture director, would-be actress Phyllis La Font, newlyweds Kay and Marvin Deving, and Captain Beegle, a retired rumrunner. In front of the suspects, Hildegarde theorizes that Forrest was poisoned and establishes that several of the witnesses had the opportunity to kill him. Soon after, Oscar arrives and discovers that Forrest's body has been stolen from the police station. Sure that the killer is always the least likely suspect, Oscar accuses the Devings of the crime until Hildegarde informs him that Tate, who had offered Forrest a drink from his whiskey flask, had been covering up the fact that his flask had a secret compartment. In addition, Kay reveals the next day that she saw the plane's pilots apparently stealing Forrest's body from the station. After Oscar unsuccessfully grills the pilots and Tate, Hildegarde discovers that Arthur T. Mack, a fellow hotel guest, has left an envelope containing $10,000 in a post office box and assumes that Arthur T. Mack is an alias for McArthur. Then, Marvin is shot and killed in the Avalon casino as he is about to reveal information about Forrest. Eventually, Oscar and Hildegarde determine that the man who called himself Forrest actually was named Kelsey, and that the real Forrest, who has arrived on the island, hired Kelsey to impersonate him. After Hildegarde finds a pack of poisoned cigarettes and confronts Mack about the murder, Mack is killed. On a hunch, Hildegarde takes Oscar to see Kay and offers her a cigarette from the poisoned pack. Kay nervously turns down the cigarette and then draws a gun on Hildegarde. Overcome by Oscar, Kay confesses that Marvin had slipped Kelsey a poison cigarette on the plane, then was murdered by Mack, whose crime was avenged by Kay.