Blood-soaked bodies of an elderly man and a woman were recovered from their residence at Sonarpur in South 24 Parganas district on Saturday, police said.
Basudeb Ganguli, 76, and his step-daughter Sumita Pandit, 38, were found in a pool of blood at Sukanta Sarani, when police arrived at the house after a domestic help informed neighbours, they said.
The four-year-old son of Sumita Pandit has said his parents were engaged in a heated argument prior to the incident, according to a police officer.
Sumita Pandit's husband is missing and search is on to trace him, he said.
Further investigation is underway.