72-year-old Asaram was later produced before District and Sessions Judge (Rural) Manoj K Vyas who remanded him to one-day police custody.
Asaram will be taken to his Manai ashram, 30 km from Jodhpur, where the police will try to recreate the scene to verify the charge against him, Jodhpur Police Commissioner Biju George Joseph told reporters here.
There are still some issues that need to be worked out for a "water-tight" case against Asaram, he said.
Doctors will also carry out a potency test on Asaram, who has denied rape charges lodged against him by the schoolgirl, the police commissioner said.
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He refuted reports that Asaram was on a hunger fast and refusing to eat or drink anything. "He is taking food and water," Joseph said.
Asaram was brought by Rajasthan police team led by Additional Commissioner of Police Satish Jnagid. They were flown via Delhi in an Air India flight at about 1230 hrs.
Unprecedented security arrangements were made at the airport.
Asaram's supporters shouted slogans at the Delhi and Jodhpur airports.
A report from Mumbai said they also stopped trains at Ulhasnagar's railway tracks in the neighbouring Thane district shortly after noon.
Asaram was arrested by the Jodhpur Police after midnight from his ashram in Indore and escorted by a large posse of police personnel to the airport, where he spent the night on a sofa in the VIP lounge.
His arrest followed an FIR filed by the girl alleging she was sexually assaulted by Asaram at his ashram in this Rajasthan city.