How to demand for a cbi investigation in a murder case

You can move to the high court for writ,order or command.The concerned high court may interfere with case and pass an appropriate order in the same to conduct free and fair investigation.Govt. will definitely sanction CBI probe if there is gravity in the case and nothing has been taken seriously on the part of authorities.

Its file an Applicable to home ministry up Gov.
Same Application may also send to Governor as well as Chief minister up.
After few days again send the reminder atteached the copy of aforesaid application.
If they don't pay any heeds.
Finaly approached the Court for the order seeking the investigation by the C.B.I or any fair agency .
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Approach high court if you are not satisfied with investigation report and ask for cbi investigation if your case little bit required the court will order for the cbi investigation. There is need a further discussion along with documents support.

we can call CBI for investigation in our personal matter when the state police fails to be competent. But we cannot call them for our petty matters and just on the basis of doubt or because we are not impressed by the way our local police are investigating.