The girl allegedly was raped by a group of three to four boys in an initial incident, Kumar said. The others learned of the rape and threatened to expose it, then also raped her, he said.
The victim filed a complaint on July 6, Kumar said. The police have arrested the principal, two teachers and four minor boys, he said.
"We are investigating," said Vijay Kumar Verma, deputy inspector general in Saran, a district of Bihar state. "We will take warrants out from the court and conduct raids" to catch the rest of the boys.
The suspects deny involvement in the incidents, Kumar told CNN.
"They are saying that they are innocent and they have not done it," he said.
The alleged incident is the latest in a string of violent sexual assaults on minors reported in India.
About 100 sexual assaults are reported to the police in the country every day, according to the National Crime Records Bureau. In 2016, more than 55,000 women, including minors, were raped across the country.
In April, massive protests broke out as demonstrators took to the streets to protest the rape and murder in January of an 8-year-old girl in the northern state of Jammu.