Northern Territory Police have conceded they failed to properly investigate the alleged murder of an Indigenous woman in central Australia, but have flatly rejected suggestions it was due to institutional racism.

Key points: Police did not declare the death a major crime until 2017

Police did not declare the death a major crime until 2017 Investigation into a non-Indigenous murder case in Darwin received around 'double the number of detectives', lawyer says

Investigation into a non-Indigenous murder case in Darwin received around 'double the number of detectives', lawyer says Coroner Greg Cavanagh highly critical of destruction of DNA evidence

Sasha Green died from a stab wound to the thigh in Tennant Creek in 2013, which nicked the femoral artery, causing her to bleed out.

The police response was heavily criticised by Ms Green's family, who said too few resources had been dedicated to solve the case because their daughter was Indigenous.

A coronial inquest is now looking into Ms Green's death and police have since successfully applied for a suppression order on most details examining their response.

But in her closing submission, the lawyer representing police, Stephanie Williams, conceded mistakes were made.

"There are many areas where the Northern Territory Police could have done better," she said.

The inquest was told those areas included:

Sending a relatively inexperienced detective constable to investigate, before pulling him out of Tennant Creek after only a week

Not returning to the town for eight months

Releasing the prime suspect too early, which potentially allowed him to interfere with evidence and intimidate witnesses

Waiting too long to search crime scenes

Searches of crime scenes not being rigorous enough

The accidental destruction of DNA evidence

Poor supervision of the investigation

Poor media management

No convincing explanation for failure to declare death a major crime: lawyer

But one of the key errors was not declaring the death a major crime, Ms Williams said.

That would have afforded investigators more resources, accountability and oversight over the investigation.

The case was only declared a major crime in 2017 — four years after Ms Green died, and only a few weeks before the coronial inquest began.

NT coroner Greg Cavanagh was highly critical of the destruction of DNA evidence ( ABC News: Steven Schubert )

The lawyer representing the Green family, John Lawrence SC, said there was no convincing explanation given as to why that declaration did not happen.

He said it appeared the paperwork got blocked at the office of Superintendent James O'Brien, who has since been promoted to the rank of Commander.

Mr Lawrence said the only explanation of the police's multitude of failures was "institutional racism".

"Aboriginal people are still considered by many as unworthy, as second-class citizens, and that's the explanation as to why once again these investigations into killings of Aboriginal women and children don't get the attention they deserve," he said.

Mr Lawrence compared the investigation to that of the murder case of Carlie Sinclair, a non-Indigenous woman who was killed by her husband in Darwin in 2013.

He said there were about double the number of detectives in that investigation, and nine police media releases, compared to just one in Ms Green's case.

"I thought in my mind it could be racism, that's the reason why they took so long, four years and a half," Casper Green, Ms Green's father, said outside court.

"[The police] should all get their act together and start looking at killings of Aboriginal people everywhere. We all live in Australia. It doesn't matter what colour we are."

'I don't understand why it continues to happen': coroner

Coroner Greg Cavanagh lashed the police for appearing not to have learnt lessons from previous inquests.

He said the investigation into Ms Green's death was "eerily similar" to that of eight-year-old Kieffen Raggett in Borroloola in 2007.

He said in that investigation, police also sent inexperienced investigators, who drew the wrong conclusions early on.

And he was highly critical of the destruction of DNA evidence, which was done without consulting the coroner's office.

"I don't want to have another inquest where forensic material of relevance has been destroyed," he said.

"I don't understand why it's happening and it continues to happen," he said.

Mr Green said he hoped the coronial inquest would lead to police soon charging the man he believes killed his daughter.

"When he gets locked up then my daughter can rest in peace, myself, my partner, we can get on with our life," he said outside court.

"I've been fighting, struggling four years and a half for my daughters case to find the killer and put him away, it's been such a long time for me.

"Find the charges, lock him up, put him away for good."