In a Lonely Place by Dorothy B. Hughes

Postwar Los Angeles is a lonely place where the American Dream is showing its seamy underside—and a stranger is preying on young women. The suggestively named Dix Steele, a cynical vet with a chip on his shoulder about the opposite sex, is the LAPD's top suspect. Dix knows enough to watch his step, especially since his best friend is on the force, but when he meets the luscious Laurel Gray—a femme fatale with brains—something begins to crack.