Laura (1944)

Detective Lieutenant Mark McPherson (Dana Andrews) investigates the killing of Laura Hunt (Gene Tierney), found dead on her apartment floor before the movie starts. McPherson builds a mental picture of the dead girl from the suspects he interviews. He is helped by the striking painting of the late lamented Laura hanging on her apartment wall. But who would have wanted to kill a girl with whom every man she met seemed to fall in love? To make matters worse, McPherson finds himself falling under her spell too. Then one night, halfway through his investigations, something seriously bizarre happens to make him re-think the whole case.

IMDb: https://www.imdb.com/title/tt0037008