Anil Kumar, an attendant, and jail warder Vivekanandan had been arrested and remanded in connection with the murder.
In the report, the Crime Branch said there were 77 bruises on Singh's body. He was beaten up by the duo on August 4 after he clashed with another inmate, it said.
Satnam was allegedly beaten up with a cable wire and his head smashed against the wall, the report said.
He was found unconscious in his cell by evening and was rushed to the medical college hospital. However, his life could not be saved.
Four inmates who witnessed the torture and allegedly joined the two in beating up Satnam, would later be taken into custody for questioning after getting permission from the court, police said.
Mann was arrested and remanded to judicial custody on August 1 after he tried to barge onto the podium of spiritual leader Mata Amritanandamayi at her Amratapuri Ashram at Vallikkavu in Kollam district while she was giving blessings to devotees.
He was stopped by devotees and security guards and handed over to police, who later admitted him to the mental hospital as he appeared mentally disturbed.