Police said the lone male member of the family Soumendra Guin went out to buy food and the two women bolted the door of the fourth floor flat from inside.
On return he found the door open and discovered the bodies of his wife and 20-year-old daughter lying in pool of blood inside the apartment with their throats slit at Subhasnagar area in the northern suburb.
Guin, who was in state of shock, could not be interrogated by the police about circumstances, possible motive and if the family had any enemy, a top officer said.