According to an FIR filed by the girl's family at the Hili police station, the jawan molested her when she was returning home from tuition last morning.
The BSF has rubbished the claim.
Soon after returning home the girl tried to commit suicide by tying a cloth around her neck, the FIR said.
The family members broke open the door and took her to the Hili Gramin Hospital in a serious condition. At around 11 pm she died in the hospital, the police said.
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Meanwhile, a senior BSF official speaking to PTI from Siliguri rubbished the involvement of any of its personnel in the incident and claimed the girl was "caught by jawans while she was trying to smuggle in a new cycle from across the border".
"The girl was caught by our jawans when she was trying to smuggle a brand new cycle from across the border. And when the bill she produced turned out to be a fake one of our jawans asked her to stay there. In the meantime, her mother came to the spot and slapped the girl. Our jawans let her go but kept the cycle there," the BSF officer said.