Hit and Run, by Richard Deming (epub/Kindle/pdf)
He never should have gotten into it in the first place. But when you need money, sometimes you do things you wouldn't ordinarily think of doing. Nothing illegal, nothing like blackmail, something just a shade this side. At least that was the way Barney Calhoun had it figured. It looked like the easiest ten thousand bucks he'd ever make. And she was lovely, though in the end she led him to murder...
An ex-cop turned private eye ought to know all the answers on how to commit the perfect crime. But somewhere along the line, he slipped up, and before he realized it they had him where the hair was short.