An Oldie But A Goodie by Richard Lockridge

Die Laughing by Richard Lockridge was published in 1969. When well known actress  Jennifer Singleton who is starring in a current play is found dead and her young gardener is caught running away from the scene covered with blood it looks like an open and shut case.  However, Lieutenant Nathan Shapiro's wife is Assistant Principal at the school Roy Baker attends and does not believe he could have killed Ms. Singleton.  Lieutenant Shapiro receives permission from his Captain for Shapiro and his partner Tony cook to look into the case. When they do they find ex-husbands and script writers mixed up in what should have been a simple case.