How does the detective's investigation shape the plot of Laura?

In the film noir classic Laura, the investigation conducted by police detective Mark McPherson serves as the primary engine for both the mystery and the film's exploration of obsession.12

As McPherson probes the murder of a woman believed to be Laura Hunt, he meticulously examines her life by interviewing those closest to her, including her mentor, Waldo Lydecker, and her fiancé, Shelby Carpenter. These interactions, presented through flashbacks, letters, and a haunting portrait of the victim, allow McPherson to construct an idealized version of Laura. Consequently, the investigation shifts from a standard police procedural into a psychological study, as the detective becomes romantically obsessed with the woman he is investigating.12

The plot reaches a turning point when the supposedly dead Laura reappears, forcing McPherson to confront the reality behind his fixation. His investigation ultimately reveals that the victim was a different woman killed by the jealous Lydecker, leading to the film's climax as the detective works to protect Laura from her former mentor.1