The incident came to light on Friday when the body of the victim was recovered from a roadside in Malwadi village under Bhilawadi police station limits, police said. Four persons have been detained and are being questioned.
"The victim had left her home on the night of January 5 following a heated argument with her mother. However, her mother did not reveal this to any of her relatives, who stay nearby. The girl's father had died a few years back," a police officer said.
Inspector General of Police (IGP) of Kolhapur range, Vishwas Nangare Patil, told PTI that at least four suspects are being questioned in connection with the case.
"We have detained four persons as of now and their interrogation is on. Besides, two more people are being questioned in this case," he said.
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The girl's body was sent to a government-run hospital for post-mortem, which revealed that the victim had been raped and smothered to death, a police official said.
"A case of rape and murder was registered against unidentified persons late last night," the official said.
"Police force has been deployed in Bhilawadi considering the possibility of law and order problems," police said.
According to police, after the incident came to light, some people circulated messages on social media claiming that the accused belonged to a particular religion and caste. However, police appealed to people not to believe in any such "baseless and provocative" posts on social media.
"Since we have not arrested anyone so far, why should one give wrong information on social media. I request all the responsible citizens not to believe in such posts," Datta Shinde, Superintendent of Police, Sangli, said.