Superintendent of Police Kunal Agarwal said the bombs were hurled at Raina when the procession was passing by Shyamsundar College.
CPI(M) claimed the Trinamool Congress engineered the incident, a charge denied by the ruling party.
CPI(M) district secretariat member Uday Sarkar said the party organised the procession and submitted a deputation to Raina I Block Development Officer on alleged anomaly in the distribution of cards for implementation of Food Security Act.
After submitting the deputation, when the procession on its return journey, the bombs were hurled from the roof of Shyamsundar College's hostel by TMC workers, Sarkar alleged.
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The party has lodged an FIR, he said.
TMC's district youth wing president and observer for Raina, Subhas Mondal, however, denied any role of the party in the incident.
Claiming that CPI(M) workers terrorised the area in the name of submitting the deputation, he questioned why the procession went to the college if it wanted to submit a deputation to the BDO.
The deceased was identified as Swapan Mallik (50).
The SP said 10 people were detained in connection with the incident and a police picket was posted in the area.