The order was passed by the division bench here of justices Amreshwar Pratap Sahi and Vijay Laxmi on a PIL filed by NGO We the People through its general secretary Prince Lenin on August 2.
The court has listed the matter for further hearing on August 22.
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.
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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 petitioner has also demanded proper security arrangements on the highways, especially at night.