A coroner has slammed the actions of Families SA at an inquest into the "preventable" death of a four-month-old Adelaide girl.

SA Deputy State Coroner Anthony Schapel said Ebony Simone Napier had been "serially brutalised" by her father Bradley Napier-Tucker, before she was found dead in her cot on November 15 2011, at her Adelaide home.

Mr Schapel slammed the failure of authorities to take action after Ebony was admitted to hospital with a broken femur when she was only five weeks old, the only injury identified by child protection authorities during her short life.

"It constituted a circumstance that ought to have seen Ebony removed from her parents," he said.

"In my view, the evidence demonstrates that the investigation was a truncated and ill-informed affair that lacked proper cohesion, and which wholly failed to protect Ebony.

"The inference is overwhelming that Ebony's injuries, fatal or otherwise, had occurred at the hands of one or both of her parents."

Mr Schapel said Napier-Tucker and Ebony’s mother, referred to as only "C", both had histories of child abuse which were not taken into account.

"The investigation was carried out in the absence of any knowledge of Bradley Napier-Tucker’s background, or propensities, and so to that extent it was flawed from the outset," he said.

SA Deputy State Coroner Anthony Schapel said it was an "absurd position" for Families SA to believe Ebony was not at risk.

Mr Schapel said it was an "absurd" position for Families SA to believe Ebony was not at risk.

The baby was found after her parents informed Families SA their daughter had been lying dead at their home for a week.

During the delivery of his findings , Mr Schapel said Ebony had sustained multiple bone fractures, including spine, rib cage, upper and lower limbs injuries, before she fatally succumbed to blunt head trauma.

Ebony had 48 healing fractures and four recent injuries when she was found.

Napier-Tucker had repeatedly thrown and dropped his daughter against hard surfaces.

"There were other injuries to Ebony to which the conclusion can be drawn that she had been serially brutalised over a period of time," Mr Schapel said.

Mr Schapel said the baby was likely last seen by "any person with a sense of responsibility" on October 16 2011, a month before she was discovered.

He also revealed a hospital social worker had expressed concern to Families SA over "C", who was 17 at the time of Ebony’s birth.

Ebony was four months old when she was found dead.

Despite the cause for serious concern, the case was closed.

Mr Schapel referenced the testimony of "C", who said Napier-Tucker had abused her and her daughter "daily" from October 16 onwards.

"C believes that Napier-Tucker broke Ebony's arm that night. She describes the violence that she says he inflicted on Ebony thereafter.

"It included shaking, squeezing of the chest, bending of her fingers, hitting her over the head with a bottle and violently throwing her in various ways.

"Eventually Ebony went into what C describes as a 'vegetable state', and ultimately died. All of this occurred in the period after Families SA closed its file," Mr Schapel said.

Families SA were also told about another child of Napier-Tucker, referred to as "N", who lived in NSW and had been allegedly abused by Napier-Tucker.

Mr Schapel said the couple were known to the authorities for persistent drug and alcohol problems, repeated domestic violence incidents, and a set of characteristics that included a lack of impulse control and suicidal ideation.

The couple moved to Adelaide from Goulburn in NSW in 2010, when "C" was pregnant with Ebony.

Napier-Tucker is now in jail with a non-parole period of seven years after pleading guilty to criminal neglect.