The 14-year-old girl was raped by Constable Rajesh Yadav (48) on Holi on March 24, it said.
Next day when the condition of the girl deteriorated, she narrated the entire incident to her mother, who took her to police station but her complaint was not lodged.
Meanwhile, the accused allegedly pressurised the family to settle the matter.
The victim's father then lodged a complaint to Additional Superintendent of Police Digamber Kushwah on whose direction an FIR was lodged at Kotwali.