My Favorite Brunette(1947)

Overview:

Ronnie Jackson is a lowly baby photographer who secretly fantasizes about being a private detective. When a lovely baroness actually mistakes him for one and asks him to help locate her missing husband, Baron Montay, Ronnie finds himself agreeing. Several days later he is on death row whiling away the hours until his execution by recounting to a group of reporters the bizarre tale of how he ended up there.