A Few Minutes Past Midnight — Stuart M. Kaminsky

Toby Peters is an unusual private eye. He's already cracked cases involving Humphrey Bogart, the Marx Brothers, John Wayne and Mae West, and now is gumshoeing for the celebrated screen star Charlie Chaplin. Welcome to Hollywood.
Chaplin has cause for alarm. A sinister visitor wielding a large knife has not only rudely paid the movie legend a midnight call but also threatened him with death unless he stops production on his latest project, a film in which wealthy old women are married and then murdered for their money.
Chaplin has been warned, too, that he'd better stay away from one Fiona Sullivan. Or else. Fiona, of course, is Toby's only lead.