Intimate Stranger, by Allan Holzman

A struggling bar singer takes a job as a phone-sex operator in order to make ends meet. One night she gets a call from a man who tricks her into listening while he murders a prostitute. Then he tells her that he's going to kill her next. She goes to the police, but the detectives don't believe her. However, an ambitious uniformed cop does believe her, and together they try to track down the killer before he kills anyone else--including her.