Justice Vipin Sanghi issued the direction to the Delhi Police asking it to transfer the case to the Crime Branch.
The court, however, made it clear that its order was not in any way a reflection on the integrity of police officers who had been investigating the case till now.
The girl's father had alleged that when he was in the hospital where his daughter was admitted after being hit by a stray bullet, the police had asked him to sign blank papers which were used to "manufacture" the complaint.
He had also said that police lodged an FIR under section 302 (murder) against one Vikrant on the ground that he (petitioner) has named him in the complaint, while he had not named anyone for the firing.
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The petition, filed through advocate Akash Vajpai, had contended that the "substance of the present FIR will vitiate the trial and the investigation."
The petitioner had also said if the police during the probe finds that Vikrant was responsible for the firing, they can move against him, but to make him a "target" by means of the "manufactured complaint" was "unacceptable".
He had also claimed that the post mortem report was not given to him by the police initially, but only after he filed a PIL in the high court for curbing the practice of celebratory firing.