AUGUSTA  — A judge on Tuesday approved proposals to reduce supervision of two people who were committed to state custody after being found not criminally responsible for killing family members.

Almost three years ago, a judge ruled that Enoch Petrucelly was delusional when he stabbed his brother to death on North Haven island. He was found not criminally responsible by reason of insanity and committed in July 2009.

Now, treatment providers and evaluators at the state’s Riverview Psychiatric Center say Petrucelly, 26, has recovered enough to seek a part-time job off hospital grounds.

Justice Michaela Murphy approved the proposal during a hearing Tuesday in Kennebec County Superior Court.

Murphy capped his off-hospital time at six hours a day and 24 hours a week, telling him he has to decide how to apportion his time.

Murphy set the limits on Petrucelly after Debra Baeder, a psychologist with the State Forensic Service, which does evaluations for the court, said she would limit Petrucelly’s time away from the hospital to 24 hours a week. Petrucelly may also visit his family home in Palymra twice a month.

In a separate hearing, Murphy approved a proposal to allow Tonia Kigas Porter to reduce her contact with community treatment providers and her psychiatrist.

Porter, who was diagnosed with paranoid schizophrenia when she starved her 5-year-old daughter to death in Bangor in 1993, has made “remarkable progress,” said Ann LeBlanc, director of the State Forensic Service.