One for the Road — Fredric Brown

A small-town reporter must investigate a murder in a motel -- before he becomes the story -- in this mystery from an Edgar Award winner and “real pro” (The New York Times Book Review).
 
Bob Spitzer is a young newspaperman in Arizona, and the owner of the local motel has just called. A woman named Amy Waggoner has been found naked and stabbed to death on the premises. As the reporter and the police chief survey the lurid scene, Spitzer reflects on the fact that he once showed a romantic interest in the victim -- a fact that could put the spotlight of suspicion directly on himself.
 
His only hope for taking the heat off is to put his investigative skills to work -- not something he needs to do very often working for a weekly rag in a sleepy town -- and locate the elusive murderer . . .