I am trying to fnd a movie about a detective trying to solve a modern day crime with flahback's to the 1940's. He interviews an old man from the 1940's who is in a nursing home and appears to have had a tracheotomy (hole in throat). He asks the detective for a cigarette and the detective gives him his pack of cigaretts and a lighter - the old man then lights up from his trachea. When leaving the old man says "here's your cigarettes back", to which the detective says "No, thanks, I just quit"

I would recommend creating an imdb. I tried that to find out a name of a movie also from details, although I couldn't, maybe someone there could help you, there is a section for finding names of movies I think.

Maybe this will help you though.
Detective-Mystery Films

Dead Again (1991)