Special Judge Sangita Dhingra Sehgal directed the crime branch of Delhi Police to conduct the enquiry within four weeks and and submit its report by April 4.
RTI activist Vivek Garg had sought registration of FIR against the Transport Minister, the Transport Commissioner and others for allegedly committing offences of corruption, cheating, criminal breach of trust and criminal conspiracy.
The court said instead of FIR, preliminary enquiry has to be conducted in accordance with a Supreme Court judgment.
Earlier in the day, DCP Crime Branch Kumar Gyanesh appeared before the court in pursuance of its summons.
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He told the court that an FIR has already been registered against Dinesh Yadav, the owner of the bus in which the 23-year-old girl was gangraped and the police is already probing the role of transport department officials in issuing him permits and licences on the basis of forged documents.
Yadav, 35, was arrested on January 2 and booked for cheating, criminal conspiracy and giving false statement on oath. He had allegedly submitted false information to the State Transport Department to get the registration certificate and the permit for the bus.