Her parents reported the crime to the local village council who chose to impose a $750 fine (50,000 rupees) and 100 situps to each of the perpetrators.
Bhuiyan and his accomplices then allegedly attacked the girl's parents before setting their house on fire with the girl inside.
"Since the victim has died, the police are now relying on what the parents and the village elders (with whom the girl had spoken) would have to say, before they can provide something more definitive to the public", she said.
The incident is alleged to have taken place in a rural village in India's northeastern state of Jharkhand.
The family said they approached the village council on Friday seeking justice, he told CNN. The head of the village council has also been arrested.
The accused and the victim knew each other and the police is investigating the case from all angles, he said.More news: Giuliani will 'get his facts straight'
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The men were enraged by the penalty, Ram said.
The accused entered the girl's house when she was alone and raped her, Officer-in-Charge, Pakur Town police station, Indrasekhar Jha, said. An autopsy will be performed to determine the girl's primary cause of death, according to local police.
The Times of India reports that Jharkhand Chief Minister Raghubar Das has condemned the events, adding in a statement that he was "shocked over the gruesome incident" and that there is "no place in the society for such ghastly acts". About 40 percent of the cases involve child rape.
An 11-year-old girl was lured away from a wedding before being raped and murdered. The government is criticized for lack of policy, can prevent cases of sexual abuse and violence against children.
While the government has passed a series of laws increasing punishment for rape of an adult to 20 years in prison, it's rare for more than a few weeks to pass without another brutal sexual assault being reported.
Protests have been held across the country since horrific details emerged last month about an eight-year-old girl being gang-raped and murdered in the state of Jammu and Kashmir.