Miss Withers, Edna May Oliver, discovers the dead body of her colleague, music teacher Louise Halloran, in a quiet schoolroom. She summons her old friend, Inspector Piper, James Gleason, but by the time he arrives, the corpse has disappeared. Having watched the only entrance (besides a fire exit with an alarm), Miss Withers knows the killer must still be inside. When the police search the building, Detective Donahue, Edgar Kennedy, is knocked out in the basement. Meanwhile, Miss Withers notices various clues, including a tune on the blackboard in Halloran's classroom. The body is found burned in the basement furnace, and then the fire alarm goes off—the murderer has escaped.
Otto Schweitzer, Frederick Vogeding, the school's janitor, had a quarrel with Halloran over money. MacFarland, Tully Marshall, the head of the school, who is a womanizer, asks Miss Withers to investigate but oddly hints she should leave town to check Halloran's relatives. Snooping around, she finds a fragment of a burnt love letter from him to Halloran. In the dead woman's apartment, which she shared with her friend and school secretary Jane Davis, Gertrude Michael, Miss Withers uncovers that Halloran held one of the Irish Sweepstakes tickets. A newspaper story notes the ticket is for the race’s favorite and could be worth $50,000 now and up to $300,000 if the horse wins. Davis claims she had a half share in the ticket, giving her motive for murder. Addison Stevens, Bruce Cabot, another teacher, admits Halloran was attracted to him, and MacFarland suggests Withers leave town to pursue relatives—but she presses on. A burnt fragment of a love letter from Stevens to Halloran is found, strengthening the suspicions around him.
Later, during another search of the basement, the lights go out and someone throws a hatchet at Miss Withers’ head. After regaining her nerve, she and Piper realize Schweitzer could not be the killer, as he remains in jail—though a newspaper announces that he has escaped. They learn that Halloran was already dying from “pernicious anemia of the bones.” When Donahue comes to in the hospital, he cannot remember what happened, but Miss Withers has Piper tell the newspapers that Donahue knows the killer’s identity. The murderer then sneaks into Donahue’s hospital room to poison his medicine, but the trap is sprung. The criminal is Addison Stevens. (The tune on the blackboard spelled out the first letters of his first name.)
With no escape, Stevens drinks the poison himself but, before he dies, reveals his motive: Halloran and he were secretly married last summer. When she would not give him up, he resorted to poisoning her slowly, triggering the anemia. In a final twist, when Miss Withers calls to console Davis, she is stunned to learn that Detective Smiley North is having breakfast with the pretty woman, a revelation that adds another layer of amusement and danger to the pursuit of truth.
