The complaint was registered at Bidhanagar North Police Station Thursday against Ram Nayan Chowdhury, a student of Bidhanagar Government College in the north-eastern fringes of the city.
"We have received a complaint against Ram Nayan Chowdhury for circulating cartoons of the chief minister (Banerjee). It has been filed by Trinamool Congress Chhatra Parishad," said an officer of the Bidhanagar Police Commissionerate.
The graphics that Chowdhury shared with others on social networking site Facebook depict a caricature of Banerjee with comments in Bengali.
"Jawab mangoge to maobabdi kahenge Shilpa mangoge to shila dikhaege (If you seek answers you will branded a Maoist and if you want industries you will be shown only plaques)" reads the comment.
No police action has been taken against the student, but Chowdhury is apprehensive.
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"There is nothing obscene in the cartoon. There are dozens of people who have shared the cartoon but I am being targeted only because I am a member of the Student Federation of India (SFI)," Chowdhury told IANS.
He also said that he was being threatened, allegedly by members of TMCP, who filed the complaint against him.