Rocky, son of suspended JD(U) MLC Manorama Devi and historysheeter Bindi Yadav, is accused of shooting dead Class XII student Aditya Sachdeva for overtaking his car on May 7 this year.
"The state government is going to file an appeal in the Supreme Court challenging the bail granted to Rocky Yadav by the Patna High Court," Principal Additional Advocate General Lalit Kishore told PTI.
Asked when the appeal is expected to be filed in the apex court, Kishore said, "We are trying our best to file it by next Monday."
Police arrested Rocky from his father's mixer plant in Gaya on May 10.
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Rocky's parents, accused of sheltering him while he was on the run after the murder, were recently enlarged on bail.
Police filed a charge sheet in a Gaya court against Rocky and another accused in connection with the murder case. They have also filed charge sheet against Rocky's cousin Teni Yadav, his father Bindi Yadav and his MLC mother's bodyguard Rajesh Kumar in the murder case.
The state government had put the case on speedy trial and investigation was completed within three weeks and charge sheet filed within a month of the incident.