An official in the Law and Judiciary department said that directions have been issued to state lawyers to file the SLP.
"The government will challenge the high court verdict on its merits. The SLP will be filed within a week's time," the official said.
Maharashtra Chief Minister Devendra Fadnavis had already announced that the state government would appeal against the high court verdict that acquitted Khan of all charges.
Bombay High Court Justice A R Joshi had on December 10 last year acquitted the 50-year-old actor of all charges in the September 2002 hit-and-run case.
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The official said that the Sessions Court had admitted the statement of late police constable Ravindra Patil, while the high court in its verdict set aside the same statement of Patil.
Justice Joshi in his verdict had dealt heavily on the loopholes in the police investigations and delay in the collection of blood samples.