Kumanjayi White, 24, died in Alice Springs in May 2025 after two plain-clothes police officers held him down in a supermarket, sparking national outrage and rallies calling for an independent investigation.
His family were told in May on the eve of the first anniversary of Mr White's death that no charges would be laid, marking "an incredibly traumatic experience".
The family confirmed on Monday that they had launched legal action in the NT Supreme Court seeking answers over the decision.
They were entitled to know the reasons under the Northern Territory Victims of Crime Charter and ask for a reconsideration of the case, the family's lawyer George Newhouse said.
"They can't do that because they've never been given reasons, and they don't know who made the decision," the National Justice Project chief executive told AAP.
In May, the Northern Territory Director of Public Prosecutions said no charges would be laid due to there being "no reasonable prospects of a successful prosecution".
NT Police earlier rejected calls for an independent inquiry.
They also refused to stand the officers down or release CCTV footage of the incident, as demanded by Mr White's family led by his grandfather Ned Jampijinpa Hargraves.
Mr Hargraves said there was a lack of transparency from authorities since his grandson's life was "violently cut short".
"We said from day one that we did not trust this process," he said in a statement.
"Nobody will tell us who actually made the decision (that no charges would be laid).
"We deserve to know all the information about his death and about the process including who decided that no one should be charged and why."
Mr Hargraves said the family would keep fighting for a "genuinely independent investigation" into the death in custody.
Mr White, who suffered from cognitive impairment and was in care, died on May 27, 2025 in the Alice Springs supermarket's confectionery aisle.
Police allege he was shoplifting and assaulted a security guard.
Mr Newhouse said the family was seeking orders from the Supreme Court to identify who made the decision that no charges would be laid.
Once the family knew who made the decision and the basis on which it was made, they would consider whether to challenge the call not to prosecute, he said.
"The lack of transparency, the lack of a proper basis for the decision, the lack of a 'sorry', and the anonymity of the decision maker all give rise to serious concerns," Mr Newhouse said.
An inquest into Mr White's death will be held in Alice Springs in April 2027.
Comment is being sought from NT and Queensland Police.
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