Satnam Singh Mann, 34, was brought dead to the Medical College Hospital here last month from a mental hospital also located in the Kerala capital.
Mann was arrested when he created a ruckus at spiritual leader Mata Amritanandamayi's ashram near Kollam early last month and was charged with trying to attack her.
In a letter to the chief minister, Achuthanandan expressed dissatisfaction in the ongoing probe which had led to the arrest of two officials from the mental hospital.
"The arrested now say they are innocent. Only a thorough probe by the CBI (Central Bureau of Investigation) will help the truth to come out," said Achuthanandan.
He said it needed to be probed what happened at the ashram, in police custody, at the sub-jail and finally at the mental hospital.
Singh's relative Vimal Kishore was the first to allege that Mann was brutally tortured.
"This death has created a furore across the country and statements that Singh was not in sound mental health is not true. He was on a spiritual journey to our state. The need of the hour is a CBI probe, and I wish you will take immediate steps for it," said Achuthanandan.
Mann's family has also demanded a CBI probe into his death.
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