The clash between the supporters of the two parties took place at Jamaldaha area of the district on Sunday in which Ramjan Mian was killed and many people were injured, they said.The police, however, did not specify the number of injured persons.
A large contingent of police force was deployed in the area to maintain peace, they added.
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CoochBehar district CPI(M) leaders claimed that deceased Ramjan Mian was their active supporter and their newly elected gram panchayat member of Jamaldaha, Atabul Islamd was among the injured.
The CPI(M) leaders alleged that the clash started when Trinamool Congress workers tried to set the house of Islam on fire which was resisted by CPI(M) activists.
The Trinamool Congress has denied the CPI(M) allegations.