The attack occurred in August while the suspect and his parents were drinking alcohol, RIA Novosti reported Monday.
Investigators said after the parents complained about the man's lack of a job he doused them and the room they were in with a mixture of gasoline and engine oil and set fire to them.
The mother died at the scene and the father died later at a hospital, investigators said.
The suspect, who pleaded not guilty, "has a number of illnesses associated with the use of drugs and alcohol" but he was found to be mentally fit for trial, an official said.
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