Meet Boston Blackie (1941)

This is one of the better outings for our eponymous reformed and charming thief-turned-sleuth (Chester Morris) who on his constant quest to stay on the straight and narrow here ends up embroiled in a nefarious web of espionage amidst the arcades and rides of Coney Island. What doesn't help his staying one step ahead of the relentlessly pursuing "Insp. Farraday" (Richard Lane) is that everywhere he has been, "Blackie" seems to leave a corpse behind! Add to his complications an accidental hook-up with the very familiar looking Rochelle Hudson ("Cecelia") whom he ends up "persuading" to assist, even abet, him. The puzzle itself is a bit of a cleverly constructed jigsaw - he is left some pretty obscure clues by a dying woman and only by piecing them together can he hope to solve the conundrum, apprehend the killers and finally get the handcuffs off. A working knowledge of Morse code will help here - it works way better than semaphore in the dark!