Maigret in Montmartre

Maigret investigates the murders of two women who are seemingly unconnected yet share a mysterious bond. The first, Arlette, is a beguiling showgirl from a seedy club who arrives at the police station to report two men she overheard discussing the murder of a Countess. But Arlette is shifty and eventually rushes from the building, only to be found strangled in her apartment the next morning. Meanwhile, Maigret hears word of a Countess who has also been found strangled, her valuables untouched and only a few mysterious leads for the detective to follow up. What connects the two? And should Maigret have done a better job of protecting Arlette when she came to him in her hour of need?