The six-month-old girl drowned in the bathtub of a North Strathfield home in November 2010 after months of obsessive worrying by her mother that the girl had dwarfism.

The woman, who cannot be named for legal reasons, appeared in the NSW Supreme Court on Wednesday.

Crown prosecutor Mark Hobart, SC, accepted the manslaughter plea on the basis the woman was suffering from a substantial impairment, being a schizophrenic disorder, at the time.

The plea follows 5?? years of legal proceedings, during which time she was declared unfit to stand trial.

Following psychiatric treatment, in December 2015, she was found to have recovered sufficiently to be tried.

At an earlier hearing, the court heard the mother phoned triple-zero just after midday on November 18, 2010, saying her baby was underwater in the bath, but told the operator "I can't go in there."

An autopsy revealed the baby had marks on the back of her head consistent with fingernail scratches.

Later that day, the woman was admitted to the mental health section of Concord Hospital.

Soon after the girl was born in April 2010, the mother had begun worrying obsessively that her daughter had genetic abnormalities.

The baby was tested for conditions including achondroplasia, the medical term for dwarfism, after the mother raised concerns about skin tags, a flat nose, and the shape of her forehead.

Though the examinations cleared the baby of any condition, the mother remained highly anxious and doctors arranged X-rays and genetic testing to ease her concern.

By the end of October, the woman had been assured all the tests were "normal".

During the months of testing, the mother spoke a lot to friends about the way her baby looked and what might be wrong with her. One friend said she brought the girl to a child's birthday party on a warm September day dressed in a hooded suit to hide the skin tags.

In the days before the child drowned, the woman continued to obsess.

When one friend got "fed up" and told her she wasn't dealing with something like cancer, the mother replied: "Sometimes it's better to deal with a terminal illness than to live with a dwarf for the rest of your life."

Forensic examinations of the woman's computer showed she searched the internet for terms including "drown", "infanticide", "suffocate", "smother" and "sudden infant death".

In February 2014, she was found unfit to be tried.

In December 2014, at a special hearing, NSW Supreme Court Geoffrey Bellew found, on the limited evidence available, that she had committed the offence of murder.

He ruled she could be detained at a facility chosen by the Mental Health Review Tribunal for a maximum of 20 years.

By December 2015, the woman's condition had improved and the tribunal found she was fit to be tried.

At a hearing in July last year, the prosecution and defence confirmed she was well enough to be considered fit to stand trial.

Several expert psychiatric reports found antipsychotic medication had significantly reduced her symptoms of schizophrenia.

She is on conditional ball and living as an inpatient at a forensic unit in western Sydney but is allowed supervised day leave.

A sentencing hearing before Justice Robert Beech-Jones will be held later this month.