Bogra police have also arrested Tufan's accomplices Ali Azam Dipu, Rupom and Atik on charges of abetting the rape.
Bogra Sadar Police Station OC Emdad Hossain said the law enforcers made the arrests on Friday in a case filed by the mother of the girl.
The girl is being treated at Shaheed Ziaur Rahman Medical College Hospital in Bogra, the police officer said.
According to the case dossier, the girl passed SSC examination this year.
Tufan raped the girl on July 17 and several times later, promising her admission to a good college. The others abetted the rapes, the OC said.
"They beat up the girl and her mother and later released them after shaving their heads," OC Emdad said, referring to the case files.
Rumki is a councillor of Pabna municipality.
The OC said Tufan admitted to raping the girl in initial interrogation.
Asha, Rumki and the other miscreants are charged with abduction and assault of the girl and her mother.