The girl was reported missing on Tuesday evening when she had gone to the fields to collect fodder for cattle, they said.
Superintendent of Police Arvind Sen Yadav said the girl died due to strangulation.
"The dead body has been sent for postmortem examination by a panel of four doctors and the entire proceeding will be videographed," Yadav said.
The victim's clothes were recovered at some distance from the body, which prima facie indicate murder after rape, he said.
Citing statements of the girl's family, Yadav said a case of family feud has also come to light and we will probe this angle also.
The SP said appropriate action will be taken after the postmortem.