A bench of Chief Justice N V Ramana and Justice Jagmohan said, "We direct the District Judge North West to conduct an inquiry..."
"We will fix the responsibility. Whether the negligence was on the part of police, health department or the judge, we will pass the order," the bench also said.
Expressing displeasure over the incident, the bench said, "You stop giving medicines when people are alive but at least do your job when they die..."
Taking serious note on the lapse, the high court had earlier demanded an explanation on why the postmortem of the murder accused was delayed.
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The court had sought the jail administration, the local SHO and the magistrate concerned's reply on it.
Shifting the blame, police had claimed that the delay was on the part of dealing magistrate S K Sethi in passing orders.
The petition, filed by Avadh Kaushik, said that Gaurav, along with his brother Rahul, was facing trial before a Rohini court in a 2012 murder case.
"Despite repeated requests, neither police nor jail authorities came to explain the facts and further procedure to the family members of the deceased prisoner nor any hospital authorities took any step for conducting a post-mortem of the body of the prisoner," the petition alleged.
"It was told that November 15 being a holiday on account of Muharram, nothing can be done. Since then, nothing has been done and the family members and relatives of the deceased prisoner are still sitting in the corridor of the hospital...," Kaushik had said and sought the high court to conduct the autopsy of the deceased immediately.