Disrupting a discussion on the acute dengue situation in the city, the corporators broke into a scuffle after a heated exchange.
This is the fourth consecutive monthly council meeting of the civic body ending amid disruption without transacting any business.
Two councillors, one each from Congress and BJP, registered separate police complaints at the Purighat police station accusing the rival party members of criminal misconduct.
"We have already registered two cases in this regard", the Purighat police inspector Tapas Chandra Pradhan said.
Similarly, Itishree Das, one of the named accused in Sethy's complaint, has also filed a counter case against the latter, the police said.