CB-CID submitted that investigation was in the final stages and sought more time.
Accepting the submission, Justice S Nagamuthu of the Madurai bench ordered the CB-CID to trace the culprits before October 28 and bring the case to an end.
Ramajeyam's body was recovered with severe head injuries on the banks of the Cauvery in Tiruchirappalli district on March 29, 2012.
This is the second time that the court has granted CB-CID time in the case.
CB-CID Superintendent of Police P S Anbu was present in court to assist the court on the petition.