The incident was reported from Baruipara in Kankinara area on Monday night.
Claiming that the victims were their supporters, the state's ruling Trinamool Congress district President and Minister Jyotipriya Mallick alleged that bombs were hurled at them by miscreants backed by the Bharatiya Janata Party (BJP).
BJP's Barrackpore MP Arjun Singh, however, denied the allegations.
The incident took place when the family members of Mukhtar were sitting outside their house, police said.
Halim died on the spot while Mukhtar succumbed at the hospital, police said. Mukhtar's wife who was critically injured was undergoing treatment at a hospital along with the other two, the police added.
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