The Senate has supported a joint motion calling on the West Australian Government to publicly release CCTV footage of an Aboriginal woman in police custody in the two days leading up to her death.

Yamaji woman Ms Dhu died after being taken into custody at the South Hedland police station in August 2014 for non-payment of fines.

She was taken to the Hedland Health Campus three times during her detention, and died on her final visit.

Earlier this year, during an inquest into Ms Dhu's death, state coroner Ros Fogliani ruled out releasing vision of her death, saying it could cause her family further trauma and distress, despite pleas from Ms Dhu's family.

The family renewed calls for the footage to be released following an ABC Four Corners program which revealed severe mistreatment of teenage boys at the Don Dale Detention Centre in the Northern Territory.

In the Senate today, a joint motion by Greens Senator Rachel Siewert and Labor Senator Sue Lines called on the State Government to respect the wishes of Ms Dhu's family and make the CCTV footage of her death available to the public.

It also called on the Federal Government to work with state and territory counterparts to implement the recommendations of the Royal Commission into Aboriginal Deaths in Custody in full, in a bid to prevent future deaths.

The motion was supported and passed.

Family welcome Senate call

Ms Dhu's grandmother Carol Roe welcomed the Senate's response.

"Let it show, let it be out there for the public," she said.

"They've got to know how my granddaughter was treated."

While the motion cannot compel authorities to release of the footage, it is hoped it will aid in pressuring the coroner.

But WA Attorney General Michael Mischin said the motion was pointless.

"The CCTV footage from the South Hedland police lockup was surrendered to the coroner as part of the coroner's brief, and so the material isn't held by the State of Western Australia, it's the property of the court," he said.

"The police don't have it anymore, and therefore aren't able to release it, and the State Government can't force the coroner to do so.

"It's interesting to hear what the Senate has to say about it, but the evidence is the property of the court and the court has made an order limiting its use."

Ms Siewert rejected the state's response and said it needed to urge the coroner to reverse her decision.

"They should go back to the coroner and ask the coroner to release that footage because the family are calling for it to be released," she said.

"Releasing this footage will not only help the family, but it will help Australian's understand what is going on in our justice system."

Coroner Ros Fogliani is expected to deliver her findings from the inquest later this year.