The body of the 16-year-old girl was found hanging from a tree on Tuesday morning near Taparpurwa village in the district, about 130 km from state capital Lucknow, they said.
The incident triggered an angry outburst from leaders of various political parties, who slammed the Samajwadi Party government in Uttar Pradesh, saying that the law and order machinery is "hanging from trees".
Police said earlier her parents suspected it to be a case of suicide.
Her father then lodged a complaint with Nighasan police, naming two youths of his village for committing the crime.
"A case of rape and murder has been lodged against the two youths -- Manoj and Dharmesh -- on the basis of her father's complaint," Station Incharge Ram Kumar Yadav said.
Kheri SP Arvind Sen Yadav told PTI that police has arrested the two youths.
Yadav himself visited the village and talked to the aggrieved family members, who told him that the two youths had earlier teased the girl following which her father had beaten them up.
However, CBI later filed a closure report in the case saying that the girls had committed suicide.
Reacting to the latest incident, opposition parties attacked the UP government for the "deteriorating" law and order situation.
"The entire state has turned into a jungle raj. People are feeling insecure...Crime graph has shot up. We wanted to raise the issue in the state Assembly, but the government is avoiding a debate on it," senior BSP leader Swami Prasad Maurya said.
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