Thirty-year old Indrajit Singh was shot at from point blank range at a polling booth near Katwa bus stand in Burdwan district. He died on the spot.
District Magistrate Saumitra Mohan confirmed the death and has sought report from the polling officials.
Meanwhile, the Trinamool Congress alleged Singh, a party supporter, was shot dead while trying to prevent booth jamming at Ward no 14 by a gangster.
SP Kunal Agarwal said, there were reports of bombing from several wards in Katwa and police were verifying the claims.
At Titagarh in North 24 Parganas district, a 55-year old man sustained bullet injury while standing in queue before Andhra Vidyalaya in ward no six.
The voter Panchu Sonkar (55), who suffered bullet injury on his foot, was taken to the local B N Bose Hospital and was now in stable condition.
A senior district police officer confirmed the incident but said the identity of the accused was not known.
Meanwhile, OSD, State Eleection Commission Sabyasachi Ghose said, "We have received reports of the two incidents but are yet to get any confirmation. There have been incidents of violence in various parts of the state where the polls are on.
"Whenever we are receiving any report or complaint we are asking the appropriate authorities to take action," he said.
A state police official said, shots were fired at a CPI(M) candidate at ward no 2 in North Dumdum Municipalty area.
Polling for the civic bodies began at 7 am today for which 35 companies of central forces besides state forces have been deployed.