Both the incidents happened Sunday night in Asansol, a city in Burdwan district.
"A woman and her child were killed and five others of the family were injured after a three-storey building collapsed, while a man was killed and another injured in a shop collapse," Commissioner of Police (Asansol-Durgapur) Vineet Kumar Goyal said.
The injured were admitted to a hospital.
Earlier on Sunday afternoon, two people were electrocuted when a puja marquee collapsed following heavy rains.
Several parts of the state have been witnessing heavy rain accompanied by strong winds since the past 48 hours in the wake of cyclonic storm Phailin which swept coastal Odisha Saturday night.
--IANS (Posted on 14-10-2013)