The Girl at Central

Molly is the local switchboard girl, and has a bad habit of listening in to people's phone calls -- especially those involving Jack Reddy, upon whom Molly has a distinct crush. But Jack has eyes only for the flighty, flirtatious heiress Sylvia Hesketh. Finally Sylvia decides to elope with him, but before that scheme can be put into action Molly hears someone else try to set up with her an alternative liaison, cutting John out of the picture. Sylvia doesn't turn up for her rendezvous with Jack, and hours later is found at the side of the road over a hundred miles away, her skull bashed in... (Goodreads)