IGP (North Bengal) Anuj Sharma has been asked to conduct the inquiry and submit the report within two weeks with the specific observation of the IGP, Commission sources here said.
The first year student, Santosh Sahani, was arrested on April 10 after a clash between Trinamool Congress and Left supporters in Siliguri.
He fell ill while in judicial custody on Monday and was admitted to the North Bengal Medical College and Hospital.
The police had stated that the jail authorities should be questioned as he was in judicial custody and it was not a police matter.