NSW Police are poised to put an application to the state's Attorney-General in a matter of days for the unsolved Bowraville killings to go back to the NSW Court of Criminal Appeal.

While the move has the full support of the police, it is unclear if it will get the same response from the NSW government, which has resisted calls to tweak the double jeopardy laws that would allow a retrial of the main suspect.

Family of the three children - Colleen Walker-Craig, 16, Evelyn Greenup, 4, and Clinton Speedy-Duroux, 16 - delivered more than a dozen folders containing the brief of evidence to the steps of Parliament House on Thursday.

The three children disappeared, and were killed, in similar circumstances in the northern NSW town between September 1990 and February 1991.

In emotional scenes on Macquarie Street, relatives recounted being treated like second-class citizens and questioned about their missing children's skin colour 26 years ago.

Lucas Craig was eight when his sister Colleen disappeared from Bowraville.

"I still remember everything like it was yesterday," he said on Thursday.

"We went out and looked for her because my mother wasn't getting help from the police or anyone.

"As a family, we used to search for her in bushland, we used to do doorknocks and ask if anyone had seen her. It is something we will never forget.

"I remember crying a lot with my mum because I couldn't help her."

Mr Craig said his family's nightmare began when his mother walked in to the police station to report her daughter missing.

"Having the police judge my mother and doubt her and say she went walkabout and not take a statement from my mother until three months later ... " he said.

"It makes you question the justice system."

Relatives and friends headed into Parliament House on Thursday to watch the debate of a Greens private member's bill aimed at reforming double jeopardy laws. The bill was voted down 25-8.

It is understood NSW Police are planning to submit the application to NSW Attorney-General Gabrielle Upton as early as next week to have the Bowraville cases head back to the Court of Criminal Appeal.

Two former attorneys-general have elected not to pursue a retrial, arguing an acquitted person can only be retried if there is fresh and compelling evidence that has not already been "adduced" in court.

The main suspect, Jay Hart, a white man who lived in the town but has since changed his name, was tried and acquitted of the murder of Clinton in 1993. He was also tried and acquitted of the murder of Evelyn in 2006.

The families of the victims have consistently demanded a retrial under laws that allow an acquitted person to be retried if new evidence emerges.

They, and detectives involved in the case, believe that important leads were not explored by police at the time and have not been heard by a court.

The families were devastated last December when a review of the case by former judge James Wood did not recommend changing the double jeopardy laws.

He said the changes campaigned for by the families had the "potential to destabilise the principle of finality in prosecutions, which will impact on defendants and the community's confidence in the courts".

Greens MP David Shoebridge denied a change to double jeopardy laws would open the floodgates to other cases brought before court, referring to Britain's interpretation of the word "adduced".

"The UK courts have had this interpretation of the word 'adduced' now for the better part of the decade," he said.

"When you review all their cases, every single one has developed a just outcome.

"There are people in jail in the United Kingdom, nasty people who have done nasty things, and they are in jail because of, we would say, the correct interpretation of the word 'adduced'."