Alleging that Dhurjati Saha suffered head injuries in an attack on May 2 in the Magrahat Paschim constituency, his wife and son demanded a CBI investigation into the incident.
Senior advocate Kapil Sibal, appearing for the state government, pointed to the members of the committee that has been formed to investigate the incidents.
In his letter to Banerjee, Chowdhury said that atrocities were committed by the ruling party's cadres on Congress supporters in the Raninagar-II block in Murshidabad district.
Taking a note of the report submitted by the National Human Rights Commission (NHRC), Kolkata High Court had recently ordered a CBI probe into the violence.
The two accused -- Bijoy Ghosh and Asima Ghosh -- were briefly detained before being arrested by the probe agency, they said.
A five-judge bench of the High Court, headed by Acting Chief Justice Rajesh Bindal, on Thursday ordered a CBI investigation in all alleged cases of heinous crimes like rape and murder.
The agency sought the details of such cases from the director general of police in line with a Calcutta High Court order that directed the CBI to take over cases.
The high court granted the state government time to file the supplementary affidavits following a prayer by it.
The TMC supremo said that the election results were declared on May 2 and till May 4, she was only heading a caretaker government and took full command after swearing-in on May 5.
Suvendu Adhikari launches fresh attack against TMC, says post-poll violence eclipsed 1946 Calcutta Killings
Incidentally, the TMC on Wednesday marked its annual 'Shahid Divas' with Chief Minister Mamata Banerjee virtually addressing people during the day.
Of the nearly 2,000 complaints related to post-poll violence in West Bengal, around 69 per cent were reported from nine districts.
Making a list of alleged notorious criminals in various districts, it noted the names of a state minister, a ruling party MLA and a former MLA among others.
Banerjee also expressed surprise over the conclusion that the National Human Rights Commission arrived at in its report without taking into account views of the state government.
The report, submitted before the five-judge bench of Kolkata High Court two days ago, also recommended that grievous offenses like murder and rape should be handed over to the CBI.
The committee, which filed an initial report in a sealed cover before the court on June 30 as per its direction, sought more time for further investigation of complaints.