A 42-year-old Quincy woman has been found not guilty by reason of insanity in the tragic killing of her 8-year-old son in their home in 2011, the Norfolk district attorney’s office said.

After a trial lasting only one day in Norfolk Superior Court, Judge Robert C. Cosgrove ruled that Li Rong Zhang, who waived her right to a jury, is not criminally responsible for the death of her son, Brandon Yang, prosecutors said. The trial included testimony that the defendant suffered from psychotic depression, paranoid delusions, paranoid schizophrenia, and acute suicidality, according to the office of District Attorney Michael W. Morrissey.

“Her mental illness had a significant impact on her ability to understand the wrongfulness of what she was doing,” Zhang’s attorney, James Doyle said.

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Prosecutors alleged that Zhang had barricaded herself and Brandon in her bedroom with a large bureau in their Yardarm Lane apartment on Jan. 13, 2011, and tried to kill both of them by filling the room with carbon monoxide by burning charcoal in a wok, Morrissey’s office reported.

Zhang’s older son, who was 16 at the time, came home to find smoke coming from the bedroom, and called the Fire Department. Firefighters broke through the barricaded door and found Zhang and Brandon unconscious. Zhang survived but her son was pronounced dead that day, prosecutors said.

According to David Traub, a spokesman for the district attorney’, doctors for both the defense and the prosecution reached a consensus that Zhang should not be held criminally responsible.

“All of the evidence presented both by the prosecution and defense to Judge Cosgrove was uniform,” Traub said.

Doyle, who is from the law firm Carney & Bassil, hailed the ruling and the prosecution’s approach to the case.

“I think it was a just verdict and it recognized that it was tragedy, not a crime,” Doyle said.

“The prosecutor’s office in this case deserves credit for taking a careful approach towards what should happen here,” Doyle said.

Following Tuesday’s verdict, Zhang was transported to Worcester State Hospital, prosecutors said.

Doyle said Zhang will be held in the hospital for up to 40 days pending an evaluation, after which she will be held indefinitely or released depending on whether she is deemed a threat to herself or others. If she is held, Doyle said, she will have the right to periodic reviews.

After the ruling, Traub and Doyle said a verdict of not guilty by reason of insanity is very rare.

“It does not happen often, but it is a matter of law,” Traub said.

Traub said Zhang had been indicted for murder, which would have carried a life sentence if she was found guilty.