Mystery Madness by Otto Coontz, 1982.
While Murray’s parents are on vacation, his older sister, Blanche, is in charge of the house. One day, he calls Blanche to get a ride home from the dentist and hears what he thinks is Blanche shooting their housekeeper.
Earlier that morning, he had heard Blanche talking on the phone to someone about a gun. Then, when he calls home, a friend of Blanche’s, Harold, answers, and Murray hears a gun going off in the background and Blanche apologizing to the housekeeper and talking about blood on the carpet. When Murray gets home, his mother’s Persian rug is missing and sees what appears to be a head in a bucket under the sink in the kitchen, further proof that the housekeeper is dead and that her blood stained the carpet.
Murray doesn’t know what to do because he is sure that his sister would never shoot anyone on purpose, and he doesn’t want to see her go to jail. He consults a private detective, Mat Cloak, who he met in a doughnut shop, for help.
The detective agrees to look into the case, and along the way, he realizes that it has connections to a case that he is already investigating. What really happened to the housekeeper? Is Blanche really guilty of murder? Moreover, who is the strange man who is following Murray around?
It’s a very funny story with some twists that readers won’t be able to guess right away. Part of the mystery is pretty obvious because Blanche is a theater student, but the real mystery is one that Murray isn’t even trying to solve and the real villain is someone who Murray thinks is a victim.
The book is available to borrow and read for free online through Internet Archive.