The police prosecutor allegedly involved in the death in custody of 24-year-old disabled Warlpiri man Kumanjayi White is now involved in prosecuting his father.

Mr White, from Yuendumu, died on May 27 after being restrained by two plain-clothed police officers following an alleged altercation with a security guard at a Coles supermarket in Mparntwe/Alice Springs. He had been living in supported accommodation under state guardianship.

Three months on, his cause of death remains "undetermined".

NT Police have refused to name or stand down the officers involved, however National Indigenous Times understands one of those officers was NT Police prosecutor Steven Haig, who has continued working in Alice Springs since the incident.

In June, it was revealed Mr Haig had previously faced accusations of aggressive behaviour toward Indigenous youth workers and was the subject of complaints over the forceful arrest of a young Indigenous woman at the same Coles store where Mr White was restrained. The NT Independent also reported he had "apparently been the subject of previous complaints concerning 'use of force' and other matters".

On Wednesday, the ABC reported Mr White's father by kinship, Martin "Isaac" Jabarula White, appeared in custody at Alice Springs Local Court on charges of contravening a domestic violence order. Those charges were dismissed after being found "improperly laid" due to an administrative error. Court documents show Mr Haig had signed off on the charge.

Mr White told the ABC it was wrong for Mr Haig to be involved in his prosecution given the officer's role in his son's death.

"He shouldn't be working," he said. "My message is just: get him out of [a] job."

In a statement last week, a NT Police spokesperson said: "The Northern Territory Police Force will not be identifying any of the individuals involved in the incident. No charges have been laid in relation to this incident and the officers involved have not been stood down."

Soon after being granted bail, Mr White was arrested and charged again over the same offence while retrieving personal items from the police watch house. He spent Wednesday night in custody there.

Kumanjayi White's death sparked nationwide vigils and calls for an independent investigation — a request rejected by both NT Police and the Chief Minister, who also refused to visit Yuendumu to meet the family. The case has renewed concerns about police treatment of First Nations people and, according to advocates, the ongoing criminalisation of disability.

Shortly after his grandson's death, Warlpiri Elder Ned Jampijinpa Hargraves said: "We know that he was held down by two police... he lost consciousness and perished. But at the moment we are in the dark about what really happened."

Speaking at Garma earlier this month, Mr Hargraves again urged police to release CCTV footage of the arrest and called for an independent body to investigate Aboriginal deaths in custody.

Northern Territory Chief Minister Lia Finocchiaro has criticised senior Indigenous Labor politicians for calling for an independent investigation into the death or Mr White, saying they "should know better" and calling them "quite frankly appalling".

Independent Senator Lidia Thorpe also condemned the NT Government's handling of the case, accusing it of a "cruel, punitive approach to law and order," and said its policies have become the subject of human rights complaints.

"The NT government and NT police are not up to the job and do not have the trust of the community," she said.