The Kerala High Court had on April 2 directed the Crime Branch to submit within 10 days the progress of the probe into the case.
In a statement filed before the high court, the state police claimed that the investigation was going in the right track, "truthfully conducted without bias or malafide and supervised by a senior officer".
"Since the Special Investigation Team is conducting the investigation effectively and the main accused have been arrested, there is no necessity to hand over the investigation to the CBI or any other agency," the statement said.
Police also claimed that there was no evidence of the involvement of any higher level CPI(M) leaders in the killings, as alleged by the petitioners.
The parents had submitted in their petition that the ongoing probe was only an eyewash, that too controlled by top leaders of the CPI(M) "whose incriminatory conspiratorial role was very much evident".
Hence, police had not acted against those involved in the larger conspiracy behind the twin murders, they said.