Directing the state government to file its reply by August 10, a division bench of Chief Justice D B Bhosale and Justice Yashwant Varma also sought a report on status of probe in the case, including the "criminal antecedents, social background and political affiliations, if any", of the accused persons.
The court has taken suo motu cognisance of the July 29 incident when a group of criminals waylaid a car, carrying six members of a Noida-based family on their way to Shahjahanpur in western Uttar Pradesh, and sexually assaulted a minor girl and her mother after dragging them out of the vehicle.
A division bench of justices Amreshwar Pratap Sahi and Vijay Laxmi passed the order on the PIL filed by NGO We the People through its general secretary Prince Lenin.
The court has listed the matter for further hearing on August 22.
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The court had asked the petitioner to file details of the alleged irregularities in the case.
The petitioner filed a supplementary affidavit today entailing therein the alleged lapses in the investigation and the factors which had led to the filing of the petition showing lack of confidence in the probe process.
The other three suspects were on the run and efforts were on to nab them, she said, adding that mere lack of confidence was not sufficient for handing over the probe to the CBI even though the state government had no hesitation in doing so if the court directed.
"Let an appropriate affidavit be filed within a week. The matter shall come up (for hearing) on August 22," the court said.
The incident had sent shock waves across the country, rocked Parliament and led to widespread criticism of the law- and-order situation in Uttar Pradesh.
The Allahabad bench also sought to know from the state government whether it had any policy to ensure proper policing of the highways passing through the state and ensure safety and security of those who used these roads.
"When a person pays toll tax on a highway, he does not do so merely for using the road. After collecting the toll tax, the state becomes duty-bound to ensure safety and security of the payers," it remarked.