RIVERSIDE, Calif. — The young son of a neo-Nazi knew right from wrong when he fatally shot his father, and he, therefore, is responsible for second-degree murder, a judge ruled Monday.

The boy was 10 years old when he shot his sleeping father in the head in 2011. Now 12, he could be held in state custody until age 23.

Because he was so young at the time of the murder, the case hinged on whether he understood that shooting his father, Jeffrey Hall, 32, was wrong at the time.

The judge, Jean Leonard, of Riverside County Superior Court, noted that after the shooting, the boy put the gun under his bed; he did not cry when the police arrived, even as other family members were sobbing; and testimony indicated that he might have told his younger sister days before that he planned to shoot their father.

“These actions show the court that he knew his actions were wrong and did not want to get caught,” Leonard said in court Monday. The boy’s name has been withheld because of his age.

The trial, which began in October but was delayed for months and resumed last week, offered a rare glance into the life of a young boy whose family hosted monthly neo-Nazi meetings at their home.

The boy had been violent since he was a young child, according to testimony, beginning before his father joined the National Socialist Movement.

He hit his sisters and his stepmother, stabbed classmates at school with pencils and once tried to strangle a teacher with a telephone cord.

After he had been kicked out of half-a-dozen schools for violent behavior, his stepmother, Krista McCary, and Hall home-schooled him, McCary testified at the trial.

Hall also beat the boy regularly for years before the murder, the judge said Monday. Michael Soccio, the chief deputy district attorney, said he hoped the court would get the boy help.

He is “a little boy, and his life has been very, very sad,” Soccio said after the ruling. But he added: “I also would have been concerned had ... (he) been released. I think he’s a very dangerous boy.”

He is scheduled to return to court next month, when Leonard will most likely determine where he will be sent.

If he ends up in state custody, the boy would be the youngest person in the state Department of Juvenile Detention system, which houses minors who have committed serious crimes, a state official said.

Matthew Hardy, the public defender representing the boy, had argued that the environment in the Hall home glorified violence and that, given his young age, left the child unable to understand right from wrong.

During the trial, Hardy showed a photograph of the young boy holding a toy gun, giving a Nazi salute and smiling beside a hooded Klansman.