Deputy state coroner Harriet Grahame on Monday found the woman, who can't be identified for legal reasons, slipped through the cracks in the days before she killed her daughter at their Miller home in southwestern Sydney in September 2016.

The woman was in 2016 found not guilty of murder by way of mental illness during a judge-alone trial in the NSW Supreme Court after telling police she had drowned the infant "to get rid of the evil in her".

Ms Grahame found the woman - referred to as SP - had an acute psychotic relapse in the days before the girl's death on either September 10 or early September 11.

However, communication between health care providers was "tragically lacking" and they failed to heed warnings from her general practitioner, who had raised concerns about a "dangerous decline" in her condition, the coroner said.

"(The girl) was drowned by her mother who had recently relapsed into an acutely psychotic mental state," Ms Grahame said.

"Her mother was mentally ill and not responsible at law for her actions.

"There were significant failures by both South Western Sydney Local Health District and the Department of Justice and Communities to provide adequate care to (the girl) and her mother."

The girl, who can only be identified as AP, was discovered by a friend of her mother two or three days after she died. The toddler was wrapped in a towel in the bath.

At the time, the mother had been admitted to a Blue Mountains hospital's mental health unit after she was involved in a car crash at Leura.

She subsequently told detectives: "That wasn't my child. That was something evil in her."

Ms Grahame said AP's death was "preventable", noting that on September 9 the woman's GP had noted a deterioration in her condition.

The doctor telephoned and faxed the South Western Sydney Local Health District mental health service.

However, there was no record of his correspondence, which Ms Grahame described as a "disturbing and unexplained feature of the investigation".

She made several recommendations to the state's health and justice departments about the need for improved training and communication.

The coroner also thanked the mother - who watched the inquest findings being handed down via video link - for taking part in the process to help patients in a similar position.

"I offer my sincere condolences to (SP) and her family. I acknowledge that the pain of losing a loved child in these circumstances is profound and their grief is ongoing," she said.

"I am so sorry that (SP) was not given the help she needed at this critical time. There were numerous failures in the care and support offered to (SP) and her family in the lead up to (AP's) death."

Australian Associated Press