Follow Me Quietly (1949)

Lt. Harry Grant is leading the police investigation of a serial killer known as the Judge, who's killed eight victims in six months, all by strangulation and all only when it rains. The Judge leaves a calling card at each of the murders, almost like he is taunting the police. What is proverbially keeping Harry up at nights about the case is that he knows almost everything about the Judge, including a physical description, except who he actually is. With the physical description, what Harry believes could help them in the investigation is to construct a faceless dummy replica of the Judge, something he doesn't want known to the press. Complicating the investigation is Ann Gorman, a reporter for the pulp magazine Four Star Crime which Harry does not respect as media. Ann, who just wants to make a living as a writer, manages to be a constant presence in the investigation moving forward as she tries to get the story, an exclusive all the better.