Banerjee gave the direction at a meeting with senior police officials in the presence of Chief Secretary Sanjay Mitra, Home Secretary Basudeb Banerjee and DGP G M P Reddy, state secretariat officials said.
She suggested that each and every complaint be scrutinised carefully and without prejudice and directed the officials to strengthen police-public relations.
The meeting came three days after a Left Front delegation led by its Chairman Biman Bose met Banerjee at the state secretariat seeking her intervention to halt post-poll violence across the state.
The chief minister also asked the police officials to remain alert against forces trying to destabilise the law and order in the state, the officials said.
The meeting was significant considering that the BJP has upped the ante against the TMC government following its stellar performance in Lok Sabha election in West Bengal.