Saloni Sharma, had allegedly committed suicide in her room at the institute hostel on Monday night.
The teenager, who had been at the institute for the last one year, left behind a suicide note in which she indicated that she was being harassed by the wife of coach Siddhartha.
Two of her hostel mates, aged nine and 11, told the police that 11 of them had dinner together following which they retired to their rooms. The deceased was last seen writing something on a piece of paper.
"She had used a tie and a dupatta to hang herself. Apart from naming a few people in the note, the girl also said that she did not deserve to live...," a police officer said.
Saloni's father, Vijay Kumar, told reporters that he did not believe that his daughter had committed suicide.
"Where did she get the sari to hang herself? The roof of the room is 16 feet high, how did she reach the ceiling fan? Besides, her feet were touching the ground, which means she did not die by hanging herself," he said.
Senior Superintendent of Police Santosh Misra said the girl's family has not submitted any complaint. "We have arrested Yamini and booked her under Section 306 of the IPC. We will include the forensic report in the charge sheet," he said.
Uttar Pradesh Sports Minister Chetan Chauhan has expressed grief at the death of the shuttler. "I have asked the Sports Directorate officials to look into the matter," he added.
UP Sports College Acting Secretary Vijay Gupta said he had sought a detailed report on the death of the badminton player.
( With inputs from IANS )