Mohd Irfan (29) was arrested on Friday in the case, almost a week after raping the 22-year-old woman along with his two accomplices.
"He was taken to the Government Medical College and Hospital (GMCH) here, where his condition was stated to be out of danger," Station House Officer (SHO) Inspector Ranjodh Singh said.
Irfan, who was lodged in the Burail jail here, allegedly broke a mirror installed outside the barrack for inmates, he said.
After his fellow inmates raised an alarm, Irfan was taken to a dispensary in the jail premises. Later, he was taken to the GMCH in sector 32 here, he said.
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"His condition is stable," the SHO said, adding Irfan will be booked for attempt to commit suicide.
Irfan, a migrant from Uttar Pradesh, was residing in Zirakpur, near here.
The Chandigarh Police on Saturday nabbed two accomplices Kismat Ali and Mohammad Garib -- (both 21 years old) of Irfan from Uttar Pradesh's Amethi and Faizabad districts, respectively.
She had taken the auto rickshaw after attending a stenography class from sector 37 here.
Ali and Garib were already sitting in the auto, according to a complaint filed by the woman, the police had said.
Irfan allegedly drove her to an isolated place in sector 53 here, instead of taking her to Mohali where she had been staying as a paying guest, they had said.
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