NEW DELHI — When the bodies of two teenage cousins were found hanging from a mango tree in the northern state of Uttar Pradesh in May, the police initially said the girls had been abducted and raped, in what seemed like yet another grisly crime against women in India.

But the country’s top investigative agency announced this week that the girls, whose bodies were surrounded by a crush of TV reporters while they were still hanging from the tree, had killed themselves and that no rape or abduction was suspected.

“Our probe found that the two girls had committed suicide and weren’t murdered,” Ranjit Sinha, director of the Central Bureau of Investigation of India, told The Hindustan Times, referring to them as siblings. “The local police had erroneously conducted their probe along the lines that the sisters were killed.”

The findings put a strange coda on a case that became a symbol of what many claimed was the precarious safety of women in India. Along with the case of a medical student who was gang-raped and tortured on a New Delhi bus in December 2012, the grisly deaths of the Budaun girls, so called after the district where they lived, is seen as representing all that was wrong with India’s patriarchal culture. As recently as Tuesday, Ban Ki-moon, the United Nations secretary general, cited the Budaun case at an event celebrating an international day to end violence against women.