Showing Sunset and Sawdust by Joe R. Lansdale

When Pete Jones, the local constable, is shot dead, his widow, Sunset, finds herself in his job, investigating a series of brutal murders. Most of the townsfolk object to her wearing Pete's gun and badge, some because this is the 1930s and they think a woman's place is in the home, others because it was Sunset who blew off Pete's head in the first place. Sunset's investigation leads her and her friends into a labyrinth of greed, corruption, and unspeakable malice. Nothing and no-one are quite what they seem in Texas.