Larry (Woody Allen) and Carol Lipton (Diane Keaton) are fairly average New Yorkers who have just managed to pack their son off to University and are looking forward to a bit of piece and quiet.
However when they meet an elderly couple, Lillian (Lynn Cohen) and Paul House (Jerry Adler) down the hall from their apartment their lives are about to suddenly change. Later on in the week Larry and Carol discover that the Lillian has died suddenly leaving them in shock.
However when Carol notices that Paul seems a bit too cheerful and eager to move on in his life she begins to suspect that he may not be entirely innocent and starts her own investigation into Lillian's untimely demise.
On telling Larry her theory, he insists she is becoming fixated on what their neighbour is doing as everything she discovers about him, all his little irregularities, seem to have a simple and non-homocidal explanation attached to them - even though Carol has difficulty seeing it.
Tired of her husband's constant pout downs she enlists the help of recently divorced Ted (Alan Alda) who aids her in the investigation which inturn makes Larry jealous of their relationship and agrees to help her himself.