There's a real murder and a real mystery in Woody Allen's Manhattan Murder Mystery, but these plot pegs are used mainly to allow Allen to explore modern urban relationships. Allen plays a N.Y.C. book editor, Larry Lipton, married to Carol (Diane Keaton, who replaced Mia Farrow at the last minute, for reasons well publicized at the time).
Carol is a free spirit, ever willing to try new experiences, but Larry is a wet blanket. When it begins to look like a neighbor has killed his wife, Carol is eager to investigate the mystery, but Larry thinks her suspicions are nonsensical and doesn't want to leave his apartment.
Undaunted, Carol finds another Nick Charles in the form of family friend Ted (Alan Alda), who joins the investigation, and feels attracted to Carol and isn't afraid to let her know. Meanwhile, a writer under Larry's aegis (Anjelica Huston), who feels romantically drawn to him, also decides to join in the fun.
Slightly jealous of Carol in the face of her budding relationship with Ted, Larry reluctantly agrees to go along on her clue-hunting expedition -- and it is he who discovers the corpse, who as it turns out was killed after Carol started poking around the apartment building.