Never Kill a Client — Brett Halliday

Mike Shayne finds himself caught up in a strange conspiracy when he's invited to Los Angeles by a terrified woman

It's the end of summer and Miami is as quiet as the grave. To Mike Shayne, the city's most notorious private detective, it seems as though he'll never have another case like the ones that made his reputation: matters of life and death that can only be solved by quick thinking, fast fists, and an itchy trigger finger. And then comes the letter from Los Angeles. It holds a plane ticket, half a $1,000 bill, and a desperate appeal. Come to L.A., begs the woman who penned the letter, or it will be my death sentence.
 
Before he even lands in L.A., Shayne is enmeshed in a plot straight out of Hollywood. And when his mysterious client proves impossible to find, the detective worries he's been lured into a deadly trap.
 
Never Kill a Client is the 43rd book in the Mike Shayne Mysteries, but you may enjoy reading the series in any order.