Murder Roundabout — Richard Lockridge

Captain Heimrich hunts for the killer of a fallen Hollywood star in this classic mystery from the coauthor of the “excellent” Mr. and Mrs. North series (The New Yorker).
 
Capt. M. L. Heimrich of the New York State Police may not have the flash of hard-boiled city detectives, but there's no lead the intrepid investigator won't follow until his every hunch is satisfied . . .
 
Real estate agent Leslie Brennan is frustrated when a prospective buyer for Annette Weaver's house fails to show up on time. She becomes even more upset when she finds Annette dead in the foyer, lying in a puddle of blood.
 
Thanks to her haughty attitude, the late film actress more famously known as Annette LeBaron had made enemies out of half the town of Van Brunt, New York -- but were any of them inclined to kill?
 
Captain Heimrich intends to get to the bottom of all the drama. To do so he'll have to investigate the motives of everyone Annette managed to annoy, and with a killer on the loose and a large cast of suspects, he'd better get started right away.
 
Murder Roundabout is the 17th book in the Captain Heimrich Mysteries, but you may enjoy reading the series in any order.