The girl was seized on Wednesday by the policemen who took her to the police station and raped her, the Press Trust of India (PTI) quoted a senior police official as saying.
The complaint is being investigated. The constables are missing, he added.
Sexual violence in India has been in the spotlight since a student was gang-raped on a bus in Delhi two years ago.
The 23-year-old died days later in hospital from injuries sustained during the brutal assault, prompting global outrage.
The outcry forced India to introduce tough new rape laws, including the death penalty in particularly brutal cases.
But correspondents say the new laws have failed to prove a deterrent and reports of rapes and cases of assault on women have, in fact, gone up.
Last month, a 26-year-old Delhi woman accused a taxi driver using the web-based booking firm Uber of raping her.
The latest incident was reported from Musajhag area in Badaun – the same district in the northern state of Uttar Pradesh where two teenage girls were found hanged last summer.
It was initially reported that the girls had been gang-raped and hanged, but federal investigators later said the teenagers “took their own lives”.