Mukherjee's son Arkadeb Mukherjee had approached the Calcutta High Court demanding an impartial reinvestigation into the murder of his father.
Expressing displeasure on the lack of progress in the investigation made by the state agencies in the case, the high court had ordered the CBI to carry out investigation in the murder on March 17.
Justice Joymalyo Bagchi had directed the central agency to submit a status report after three months.
Mukherjee, son of former CPI(M) MLA from Hirapur, Bamapada Mukherjee, was shot dead in broad daylight on May 10, 2012 in Asansol town when he was out for morning walk.
The court had ordered a CID investigation in 2012 but when the state investigating agency also could make little progress in the probe, Arkadeb moved the high court again seeking a CBI investigation.
Mukherjee's father Bamapada Mukherjee was the first mayor of Asansol and a close associate of former West Bengal chief minister Jyoti Basu.