The Nurse Murders by Jon Talton

A sadistic killer is terrorizing Phoenix, and he's got Gene Hammons' number...
It's 1936, and private investigator Gene Hammons has more work than he can handle. A crime syndicate, J. Edgar Hoover, a wealthy family from back East, and a wily stalker all want something from him. His capable-but-drug-addicted brother, still a homicide detective, is as much a hindrance as a help. Luckily, Hammons finds a professional ally in Pamela Bradbury, a fellow gumshoe with some new tricks to teach him. When the two pair up, there doesn't seem to be a case they can't solve, from kidnapping to blackmail to an intricate gold-smuggling operation.
But then a young nurse with red hair is sadistically raped and killed, and Gene recognizes the signs of a "lust murderer," having famously solved the case of the University Park Strangler years earlier. When he's contacted by the killer, Hammons knows he and Pamela must work quickly to catch the brutal murderer before he strikes again. The two come to each other's rescue more than once, and as deep feelings develop between them, it's not lost on Gene that their relationship might well prove dangerous-especially for Pamela, with her lovely red hair.
Rich in atmosphere and authentic period detail, THE NURSE MURDERS is a gritty, nail-biting race to catch a killer in a city struggling to assert itself amidst the hardships, corruption, and political machinations of post-World War I America.