While staking out a boarding-house where is staying Emile Paulus, a suspect, Detective Archambaud is wounded by a bullet shot from an undetermined place. To further the investigation, Maigret, his superior, decides to put up at the boarding-house posing as an ordinary guest. He is welcomed by Mademoiselle Clément, the dignified owner, and soon discovers the various people living in the place. He also takes a special interest in a woman who dwells in a neighboring block of flats, Françoise Boursicault, the lonely crippled wife of a purser most of the time at sea... A common thread through all of them is that... they seem to have something to hide...