A Northern Territory judge who reportedly told a 13-year-old boy he had taken advantage of his mother's alleged murder when he committed property crimes will have a formal complaint filed against him.

The 13-year-old boy, whose mother was allegedly murdered by his father in January, pleaded guilty last week to property damage.

In the Tennant Creek Youth Court, Judge Greg Borchers told the boy that he accepted there had been a "significant breakdown" in the family.

"But you've duchessed it, that means that you've taken advantage of it," he said.

Following his mother's death, the boy's school attendance dropped, he abused alcohol, sniffed petrol, and suffered social anxiety, the court heard.

One night in May, the boy broke into a hotel, damaged a bank, a car and a restaurant. He had also previously been arrested for other property crimes.

"You're rampaging around the streets at night and no-one cares … you've got no-one looking after you," Judge Borchers said.

"You don't know what a first-world economy is. You don't know where money comes from, other than the Government gives it out."

He remanded the boy in custody until July 13.

"You're not going back into the community, the community can't afford you," he said.

Complaint being made to NT Attorney-General

The Central Australian Aboriginal Legal Aid Service (CAALAS) is representing the boy.

The ABC understands CAALAS and other organisations and individuals are making a complaint to the Attorney-General, the chief judge, and the NT administrator.

"CAALAS takes the matter very seriously and is in the process of formally referring this matter to the appropriate authorities," CAALAS chief executive Eileen Van Iersel said.

Judge Borchers' remarks were totally inappropriate, Darwin barrister John Lawrence said.

"What this judicial officer did and said … completely undermines the integrity and the prestige and, indeed, the honour of the court in which he sits," he said.

"For a judge to directly say that to a 13-year-old defendant in his circumstances is disgraceful.

"I don't think any adult should speak to a child like that."

Mr Lawrence, a former president of the NT Bar Association, is representing several former juvenile detainees before the Royal Commission into the Protection and Detention of Children.

"This judicial officer, believe it or not, is doing this while a royal commission is hovering over this entire legal system," he said.

"This has gone way beyond the pale, and I think it's a matter that the royal commission will hear about."

The royal commission resumes in Darwin next week.