The three were trapped inside a room when the building collapsed, they said.
Taraprasanna Saha, Sobha Rani Saha and Beauty Roy were pulled out by local residents and fire brigade personnel, the officials added.
They were taken to the Calcutta Medical College Hospital where doctors declared Taraprassana as "brought dead". The injured, who are in a critical condition, were admitted to the hospital.
It was not immediately known how they were related, and if there were others in the building.
The area was cordoned off and the building evacuated, they said.