24-year-old Puneet was produced before Additional Chief Metropolitan Magistrate Sudesh Kumar after expiry of his judicial custody and the court will hear arguments on February 6 on the plea.
The Centre had earlier opposed his plea seeking trial here saying the petition "is an abuse of the process of law" and an attempt to delay extradition proceedings.
In its reply, filed through advocates AK Vali and Naveen Kumar Matta, the Centre had said, "Tt is entirely the prerogative of the government to take appropriate decision on extraditing or refusing to extradite a fugitive criminal."
He was arrested in Punjab on November 29 last year after a court here issued an arrest warrant against him in pursuance of an extradition request by Australian authorities.
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Puneet had argued that his trial should be conducted in India as there was a threat to his life in Australia.
His counsel had claimed that Puneet was pressured in Australia into pleading guilty to the alleged offences and was afraid he would be convicted if he was sent back there.
According to the red corner notice issued against him, Puneet was driving a sedan in Australia's Southbank on October 1, 2008, at a speed of 148 kmph when he struck a concrete pillar, leading to the death of one person.
The notice also stated that Puneet had left Australia on June 12, 2009, on an Indian passport belonging to one of his friends.