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Police suspect the hanged woman was raped before being murdered, bringing to five the number of rapes reported in the past 36 hours in the state, including two women who were then killed.
"The sub-inspector accused of committing the rape of the woman has been put under arrest while we have launched a manhunt for the three constables accused of being party to the crime," a spokesman at state police headquarters said.
The latest reports come after two girls, aged 12 and 14, were gang-raped and hanged from a tree on May 27, the day after Narendra Modi was sworn in as prime minister.
The two cousins, from a low-caste community, went missing from their home in Uttar Pradesh when they went to an outdoor toilet. The next morning, villagers found their bodies hanging from a mango tree in a nearby orchard.
Workers from Modi's party clashed with police when they tried to march on the office of Chief Minister Akhilesh Yadav to protest against the violence, and opposition parties have demanded Yadav's dismissal.
Yadav has asked the Central Bureau of Investigation (CBI), the country's top crime-fighting agency, to investigate the case. The CBI on Thursday said it registered a case against three people and two police officials.
Uttar Pradesh is one of the world's poorest regions and has largely missed out on the economic boom that swept much of India over the past decade. Its population of 208 million is larger than that of Russia, and it has endured a string of revolving door governments that have pandered to narrow caste interests.
Yadav met businessmen in New Delhi on Thursday to drum up investment and said reports of lawlessness were exaggerated.
"In Uttar Pradesh, not only is the atmosphere good but law and order, compared with many other states, is also better," Yadav told reporters.
His government later issued a press release that some of India's most prominent companies, including Reliance Industries Ltd and ITC Ltd, had pledged $9.2 billion in investment in the state at the meeting.
Yadav ran his 2012 election campaign as a moderniser, advocating the use of technology to transform the state. However, his term in office has been marred by scandals over riots, gangsterism, and now, sex crimes.
His father, a former chief minister widely seen as the power behind the throne in the state, drew widespread condemnation earlier this year when he said rape laws should be softened and that "boys will be boys" - sometimes committing rape by mistake.
As in many parts of the world, conservative Indian leaders across the political spectrum frequently blame rape on the victims' dress and social behaviour.
Modi broke his silence on the issue in a speech to parliament on Wednesday, saying India needed to protect and respect women and that the government needed to act.
He also asked politicians to refrain from making comments about why rape happened. A senior member of Modi's own party last week said rape was a social issue, and "sometimes right, sometimes wrong."