The reports quoted the sources as adding that Kumar was not attending Election Commission meetings, and that he was absconding. Senior Kolkata Police officials however said that that was not the case.
The CBI team was on Sunday stopped by Kolkata Police and taken to a police station.
Five members of the team were detained, but released later.
West Bengal Chief Minister Mamata Banerjee also reached Kumar's home Sunday evening, as did the West Bengal director general of police, and Kolkata Mayor Firhad Hakim.
Kolkata: West Bengal Director General of Police arrives at the residence of Kolkata Police Commissioner Rajeev Kumar. Chief Minister Mamata Banerjee is also present there, a meeting is currently underway. pic.twitter.com/oLtLWf3ZnZ
The face-off continues to blow up into a constitutional crisis, with BJP national general secretary Kailash Vijayvargiya saying "democracy has ended in West Bengal".
He added that "CBI was investigating on orders of Supreme Court but they didn't allow them. CBI officers were detained, this is the first time something like this has happened since independence; we condemn this."
Mamata Banerjee meanwhile came down heavily on the side of Kumar.
"I still say Rajeev Kumar (Kolkata Police Commissioner) is the best in the world," she said.
"I will stand with my force. I respect them. I felt very sad today. This is the destruction of the federal structure," she added.
Banerjee added that the CBI had shown up at Kumar's home without notice. That the Kolkata Police could have arrested them, but that they did not do so.
West Bengal CM Mamata Banerjee: I am proud to say that my responsibility is to give protection to the force. Without notice, you are coming to Kolkata Police Commissioner's house. We could have arrested CBI but we left. pic.twitter.com/P7DrJjd0Yc
West Bengal CM Mamata Banerjee: BJP is torturing Bengal. They are forcibly trying to destroy Bengal just because I did brigade rally. Yesterday you saw the language of PM where he threatened. pic.twitter.com/cK57JFH56j