More than two months after the death in police custody of 24-year-old disabled Warlpiri man Kumanjayi White, Northern Territory Police say the cause of his death remains "undetermined".

Mr White, who was under state guardianship and reportedly living in supported accommodation, 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.

His death sparked vigils across the country and prompted widespread calls for an independent investigation; a request denied by both NT Police and the Chief Minister, who also refused to visit Mr White's home community of Yuendemu to meet with his family.

The incident has renewed national concern over police treatment of First Nations people and what advocates say is the ongoing criminalisation of disability.

In a statement, an NT Police spokesperson said Mr White's death remains "undetermined", adding that "a forensic pathologist is required to complete further investigation."

While police say their investigation is ongoing, they have refused repeated calls to stand down or name the officers involved, despite witness reports alleging that an officer placed a knee behind Mr White's head during the incident.

Mr White's grandfather, Warlpiri Elder Ned Jampijinpa Hargraves, said shortly after the death: "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 last week, Mr Hargraves again called for police to release CCTV footage of the arrest and demanded the creation of an independent body to investigate Aboriginal deaths in custody.

NT Police 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."

National Indigenous Times understands one of the officers involved is NT Police prosecutor Steven Haig.

In June, it was revealed that Mr Haig had previously been accused of aggressive behaviour toward Indigenous youth workers and was also the subject of complaints for the forceful arrest of a young Indigenous woman at the same Coles where Mr White was restrained.

The NT Independent also reported that Mr Haig had "apparently been the subject of previous complaints concerning 'use of force' and other matters".