Dixon “Dix” Steele (Humphrey Bogart) is a down-on-his-luck Hollywood screenwriter who has not had a hit, “since before the war.” While driving to meet his agent, Mel Lippman (Art Smith), at a nightclub, Dix’s explosive temper is revealed when, at a stoplight, he engages with another motorist in a confrontation that almost becomes violent.
At the nightclub, Mel cajoles him to adapt a book for a movie. The hat-check girl, Mildred Atkinson (Martha Stewart), is engrossed in reading the copy meant for Dix; since she only has a few pages left to go, she asks to finish before passing it on to Dix. Dix has a second violent outburst when a young director bad-mouths Dix’s friend Charlie (Robert Warwick), a washed-up actor.
Dix claims to be too tired to read the novel, so he asks Mildred to go home with him, ostensibly to explain the plot. As they enter the courtyard of his apartment, they pass a new tenant, Laurel Gray (Gloria Grahame); Dix and Laurel are clearly intrigued by each other. As soon as Mildred is convinced that Dix is not trying to seduce her, she describes the story, in the process confirming what he had suspected—the book is trash. He gives her cab fare to get home.
The next morning, he is awakened by an old army buddy who is now a police detective, Brub Nicolai (Frank Lovejoy), who takes him downtown to be questioned by Captain Lochner (Carl Benton Reid). The coat check girl Mildred was murdered during the night and Dix is a suspect. Laurel is brought to the police station, she confirms seeing the girl leave Dix’s apartment alone and unharmed but Lochner is still deeply suspicious. Although Dix shows no overt sympathy for the dead victim, on the way home from the police station, he anonymously sends her two dozen white roses. https://en.wikipedia.org/wiki/In_a_Lonely_Place