Ms Day died in hospital after repeatedly falling and hitting her head in a Castlemaine police cell in December 2017.

She was arrested more than two weeks prior for being drunk on a train.

A coroner found the 55-year-old's death was clearly preventable.

Ms Day's family is suing the State of Victoria for unlawful imprisonment and negligence.

A writ lodged in the Supreme Court alleged Ms Day's arrest and detention was a breach of her human rights and inconsistent with the Australian Constitution.

It named the eight police officers involved.

They are accused of breaching their duty of care to Ms Day. Her fatal injuries sustained in police custody allegedly amounted to negligence.

"Tanya was especially vulnerable in custody owing to her Aboriginal heritage," the documents said.

"Aboriginal over-representation in the criminal justice system is inextricably linked to ongoing and previous generations' experiences of European colonisation."

Ms Day's family is seeking damages for psychological injury, and the loss of financial, domestic and child care support.

Coroner Caitlin English earlier this year referred Ms Day's death to prosecutors, saying there was evidence to suggest it may have amounted to negligent manslaughter.

While police claimed to have conducted regular verbal and physical checks on Ms Day, Ms English found these were inadequate.

The coroner also said the train conductor's decision to call triple-zero on Ms Day had been influenced by her Aboriginality.

But she did not find the decision of police to take her into custody displayed systemic racism.

Victoria Police in August announced charges would not be laid against the officers involved, following advice from the Office of Public Prosecutions.

Ms Day's death prompted the state government to abolish the offence of public drunkenness.

Australian Associated Press