The central agency is probing the cases following instructions from Calcutta High Court.
The CBI arrested two persons today in connection with an alleged attack on a BJP supporter in West Bengal's Nadia district after the Assembly polls this year, officials said.
The accused Bijoy Ghosh and Asima Ghosh were briefly detained before being arrested by the agency, they added.
The CBI has carried out searches at 15 locations in connection with the attempt-to-murder case. Dharma Mandal suffered serious injuries while trying to save one of his relatives, who was allegedly being beaten up by the eight accused named in the complaint in Chapra on the night of May 14, officials said.
In his complaint, Dharma Mandal's brother Ayan alleged that the members of his family are known BJP supporters.
On May 14, the eight accused beat up their relative, Sanajit Mandal, and dragged him to a nearby locality, the complainant alleged. The complainant, his brother Dharma and nephew Saurav rushed to save Sanajit when they were also allegedly beaten up by the accused.
One of the accused, Ujjal Ghosh, allegedly hit Dharma on his head with a sharp-edged weapon, leaving him seriously injured, according to the FIR.
The CBI has registered 10 more FIRs in connection with post-poll violence in West Bengal, taking the total to 21.
The central agency took over the cases in accordance with the instructions of a five-judge bench of the Calcutta High Court.