Shette, 45 who was serving a life sentence, died at the government-run J J Hospital on June 23 night, sparking off a huge protest by over 200 inmates of the prison.
"This is a custodial death. It is the jail authorities' responsibility. Tell us what steps the jail officials took after her death. Why didn't they take her to hospital (immediately)?" asked the division bench of justices R M Savant and Sadhana Jadhav.
The petition also demanded that the accused should be booked under section 377 of the Indian Penal Code for committing unnatural sexual offences.
Though the petition didn't mention it, the police had earlier said Shette was allegedly tortured and a stick was inserted in her private part.
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The court today also asked the government to explain as to why the inmates had to file the first information report (FIR) in the case. "Should the inmates be lodging FIRs against jail authorities? Why didn't the jail authorities lodge a case of accidental death?" Justice Jadhav asked.
After going through the autopsy report, the bench also said the affidavit must explain as to why there were so many injuries on Shette's body.
Additional Public Prosecutor Mankunwar Deshmukh said that an inquiry has been initiated and six jail officials have been arrested.
The statement, however, didn't satisfy the court. "We are not concerned with the ongoing inquiry. We anyway know how such inquiries are conducted. We only want to know why there was a delay in taking the victim to the hospital and why the inmates had to file FIR," the court said.