Rafiq Mondal, a local Trinamool Congress (TMC) leader was killed in an attack in Ashoknagar area of North 24 Parganas district on 10 August.
Two other were also injured in the attack and the attackers are allegedly related to CPI(M).
Mondal was killed when attacked at his house by a group of people led by Mujibur Rahman of CPI(M) at Naduria, Additional SP Bhaskar Mukherjee said.
Mondal's wife and brother were injured in the attack.
Four persons were arrested in this connection, Mukherjee said adding raids are on to nab others.