A woman was found dead inside her rented accommodation at Nagerbazar in Dum Dum early on Friday.
Police said Beauty Basu was possibly strangled to death.
Her husband, Amit Basu, is missing.
A preliminary investigation revealed Amit had been married to Beauty for almost a decade. The couple have a nine-year-old son.
The police said following marital discord, the two have been sleeping in separate rooms for some time now.
On Thursday, Amit apparently told his son that the three would sleep together in a room.
In the wee hours of Friday, the boy’s cries for help alerted some of Amit’s neighbours.
When they rushed to the house, they found Beauty lying motionless. Her husband was nowhere to be found.
The police have sent the body for a post-mortem. A search has been launched for Amit.
Family members of the woman told the police that Amit, who worked as a security guard, was currently unemployed.