[quote name='Duo_Maxwell']A Dame to Kill For has some of the same characters so technically it has some little connection with the movie, but it's more a prequel to the stories used in the movies.[/QUOTE]
Well, to be even more technical, every book has characters that were in the movie, whether it's just in the background or as a primary/secondary character. They are, after all, stories about Sin City...
The movie was only The Hard Goodbye, then The Big Fat Kill, then That Yellow Bastard - in that order, with That Yellow Bastard having a section broken off and placed in the beginning. The very first scene was from the series, The Customer is Always Right and the bookend at the end with Becky and the "Doctor" was not in any story at all.