Tangentyere Council CEO Walter Shaw says it is "overkill" to have a camouflaged, specialised police unit armed with weapons performing general duties tasks in Alice Springs.

Key points: On November 9, Kumanjayi Walker died after he was shot in Yuendumu, 266 kilometres north-west of Alice Springs

TRG members have travelled to Alice Springs to support general duties police officers in the weeks following the incident

NT Police has not answered questions about how long the unit with stay in the NT town

The Territory Response Group (TRG) is part of the Australian Government's national counter-terrorism taskforce.

TRG members have been patrolling the Central Australian town to help support officers in Alice Springs following the death of 19-year-old Warlpiri man Kumanjayi Walker in Yuendumu.

WARNING: This article contains an image of Mr Walker used with the permission of his family.

"I think it's overkill having the TRG in Alice Springs or any township of the Territory for that matter," Mr Shaw said.

"I don't think it's warranted having them on general duties, I think they should be called out on very severe circumstances."

CEO of the Tangentyere Council Walter Shaw says it's "overkill" to have the TRG in Alice Springs. ( ABC News: Nick Hose )

On Monday, night a 23-year-old man was flown to Adelaide in a serious but stable condition after being struck by an unmarked TRG police car in Alice Springs.

Southern Region Commander Brad Currie said the TRG car had been conducting "proactive, general policing patrols" in the area prior to the incident.

"The TRG are here to assist us in general policing in response to a number of incidents in the last two weeks, that includes a number of criminal damage (cases) and crime and anti-social behaviour that's occurred in the town," Commander Currie said.

He also highlighted that the "serious custody incident" would thoroughly investigated.

Mr Shaw wanted to see the relationship between the NT Police and the community improve, but wasn't happy with the response from police so far.

Police maintained tight control of the crime scene in Yuendumu after a 19-year-old was shot on November 9. ( ABC News: Katrina Beavan )

"I think the incident of the recent shooting in Yuendumu and the incident of the young guy being run over on Monday, the police need to reconsider their position," he said.

"They need to look at resetting their relationship back to the community.

"I think there's a fine line between law and order and social order."

Independent Member for Stuart Scott McConnell wants to know why the TRG is performing general duties tasks. ( ABC News: Jano Gibson )

Independent Member for Stuart Scott McConnell welcomed the TRG's presence, but said the community wanted to know why the NT's elite squad was performing general duties tasks.

"We probably need the TRG in Alice Springs at this time," Mr McConnell said.

"The idea that they are out doing general duties, which is what it appears to me, is very concerning.

"We need to have the police force remaining very neutral and engaged with the community."

Mr McConnell said it was not an "appropriate policing response" to have the TRG deployed in such a way.

'Not unusual': NT Police Association

Despite these concerns, NT Police Association president Paul McCue the elite force's presence in Alice Springs was not out of the ordinary.

"It's not unusual that TRG comes to town; that's part of their role to police the whole of the Northern Territory, and from time to time they come down and support our other general duties frontline members in various matters that go on and various incident that our GDs respond to," he said.

Mr McCue said it was "no secret" there had been some tension in Alice Springs over the last few weeks.

19-year-old Kumanjayi Walker's death has triggered a coronial inquest. ( Supplied: Facebook )

On November 9, 19-year-old Warlpiri man Kumanjayi Walker died after he was shot in Yuendumu, 266 kilometres north-west of Alice Springs.

NT Police has since charged one of its officers, 28-year-old Constable Zachary Rolfe, with one count of murder.

Constable Rolfe has indicated he will plead not guilty.

Mr McCue said considering this tension, he "absolutely supported" additional help for the Alice Springs officers.

"The majority of people in the community fully support the police, there is no question about that," he said.

"We're proud of the work out police do and will continue to support them appropriately."

'Additional police resources, respite and general response'

A NT Police spokeswoman didn't answer questions about how long the TRG would remain in Alice Springs.

A rally in Alice Springs on November 14 following Kumanjayi Walker's death on November 9. ( ABC News: Mitchell Abram )

"Members from the Northern Territory Police Territory Response Group have been in Alice Springs providing additional police resources, respite and general response since early last week," she said.

"The deployment of the TRG is an operational decision based on the public safety needs across the NT."

The spokeswoman said TRG tactics and equipment was considered "operational information and not for public release".

The ABC asked if officers would be carrying military grade assault weapons while on duty in Alice Springs.

"The level and type of equipment used by TRG is determined as part of the threat assessment, however police will not be commenting on the equipment used during operational deployments," she said.