Three of Ms Day's children, Belinda, Warren and Apryl, delivered a statement outside the Coroners Court in Melbourne on Friday, on the final day of the inquest into their mother's December 2017 death.

"We have had a coronial investigation - but what we now want is a criminal investigation," they said.

"We want to know whether the police who should have cared for mum, committed an offence in denying mum her dignity and ultimately, her life."

They also said they found it "deeply offensive" to hear during the inquest that Victoria Police had not made any changes or launched a review into their mother's death.

"Victoria Police must take responsibility for Aboriginal people dying in their custody," they said.

Ms Day's children thanked the witnesses from Ambulance Victoria for giving "truthful evidence and heartfelt apologies" at the inquest, but noted neither Victoria Police nor V/Line had apologised.

Ms Day, 55, died 17 days after she was arrested for public drunkenness following a call from a V/Line conductor, who gave evidence at the inquest that he believed she was under the influence of a substance and her safety was at risk.

CCTV footage played to the court and later released to the media showed she hit her head five times while held in the cell at Castlemaine station to sober up.

EARLIER: Groans have filled a Melbourne coroners court as a senior policewoman spoke about the "good work" of the force during an inquest into the death of an Aboriginal woman in custody.

Yorta Yorta grandmother Tanya Day fell and suffered a head injury while in a regional Victorian police cell after being arrested for drunkenness on a train on December 5, 2017.

She died two weeks later.

Victoria Police Superintendent Sussan Thomas was called to give evidence on the final day of the inquest into Ms Day's death on Friday.

The officer - who is in the priority communities division and in charge of the Aboriginal and youth portfolio - was asked why she believed she was chosen to speak at the inquest.

"I am here to talk about all the good work that is occurring across Victoria Police and the policies as well," Supt Thomas said.

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Her response caused Ms Day's son to walk out of the courtroom and other family members and supporters to audibly groan.

Earlier, she was asked about whether she knew she would be asked about police training in relation to cultural awareness around Aboriginal communities.

"I knew that I was coming here to say that the training exists, but I'm not a subject matter expert on the training," Supt Thomas told the inquest.

Supt Thomas found out two days ago she would be giving evidence, the inquest was told.

The inquest before coroner Caitlin English is due to finish later on Friday.

- With AAP

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