The SFI is the student wing of the state's opposition Communist Party of India-Marxist (CPI-M).
Besides conducting an independent and parallel investigation, the WBHRC has asked the Kolkata Police to probe into the case and submit a report on it withing a week.
"We don't have any faith in the police as we all know that the SFI leader died in police custody. Which is why, we have decided to carry out our own investigation. A three-member team will conduct the inquiry," said a WBHRC official on condition of anonymity.
Meanwhile, the Left parties held demonstrations across West Bengal, including Kolkata, on Thursday to protest against Gupta's death.
Commuters faced troubles as traffic jams were reported from different parts of Kolkata as the SFI and Democratic Youth Federation of India (DYFI) conducted 15-minute road blocks on Thursday.
Demonstrators conducted road blocks in several areas of the city including Behala Chowrasta, Shyamabazar, Moulali and Sealdah.
The CPI-M has also called for a 12-hour strike in south Kolkata's Garia, Tollygunge and Dhakuria with shops shut down in those areas.
The SFI along with three other Left organizations have called for a students' strike across West Bengal.
Gupta died during a police action in Kolkata at their law violation protest on Tuesday.
Thousands of people, including former West Bengal Chief Minister Buddhadeb Bhattacharjee, joined the funeral procession of Gupta in Kolkata on Wednesday.
His last rites were performed at Keoratala crematorium in south Kolkata on the same day.
The Kolkata Police on Wednesday said a person has been arrested in connection with the matter.
The police said Gupta died after he was hit by a lamp post while alighting from the police van in which he and other protesters were being taken away after arrest.
The students had alleged that he was beaten up severely by police and pushed and even after he was taken to the SSKM Hospital he was left unattended. The students, including girls, said they were roughed up and ill-treated even inside the vehicle.
Gupta was an M.A student from Rabindra Bharati University.
The SFI was holding a protest in demand of student elections in the city's downtown area at Esplanade on Rani Rashmoni Road.
Soon there were commotion and a police action led to the clashes.
Several others were also injured in the police action and the clashes.
--IBNS (Posted on 04-04-2013)