The three victims -- an aged couple and their middle-aged daughter -- were trapped inside a room when the building collapsed, the police said.
Taraprasanna Saha (94), his wife Sobha Rani Saha (84) and daughter Beauty Saha (56) were pulled out of the structure by the fire brigade personnel with the help of the locals, they added.
They were immediately taken to the state-run Calcutta Medical College, where Taraprasanna was declared brought dead. His wife and daughter died at the hospital subsequently, Deputy Commissioner of Police, Central, Mitesh Jain, told reporters.
Two others, who were also trapped in the building, were rescued by the locals. They were released from the hospital after primary treatment.
The structure collapsed at around 11 AM. The other tenants of the building had evacuated it earlier, soon after it was declared "dangerous" by the Kolkata Municipal Corporation (KMC).
"It was not safe to reside in the building and only one family was living there forcefully," local Trinamool Congress (TMC) MLA Smita Bakshi said.
Eyewitnesses said the upper floors of the building collapsed and fell on the side where the Saha family had been living.
KMC engineers went to the spot to ascertain the extent of damage. The area was cordoned off by the authorities.
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