A BATHURST woman said her seven-week-old son and "the Lord" had told her to drown him in a bath to let him "be at peace", a court has heard.

The woman, who cannot be named for legal reasons, pleaded not guilty to murdering her child as her trial began in the NSW Supreme Court today.

She had stayed the night at her cousin's house in July 2005 with her newborn son and two-year-old daughter.

Her cousin left the following morning to go and get nappies and supplies and when he returned he found water all over the floor of the house.

"He noticed water on the floor, the kitchen taps were running and he heard taps running in the bathroom," Crown Prosecutor Peter Barnett told the court in his opening address.

"He found the deceased in the bathtub, near the plug, lying face down with water coming out of the side of his face."

The boy's mother, who had been acting strangely since the previous evening - "running, dancing, jumping around the house" - was in a bedroom, lying under a blanket with her daughter.

Later at the hospital, she told medical staff that the Lord and the boy had told her to do it, the court was told.

"She told medical staff that the child had told her to put the child into the bath ... so the child could be at peace," Mr Barnett told Justice Peter Hall at the judge-only trial.

"She said the Lord has also told her that she was to do that for her child."

But the woman variously blamed her daughter for tipping the boy out of his pram into the bath, or on to the floor, or said that she herself had dropped him.

Eventually she said that the boy was already dead by the time she walked into the room.

Police and medical staff at the hospital noticed the woman's "bizarre behaviour" and said she later admitted to using speed or amphetamines at the time of the incident.

Prosecutors said that either the woman deliberately drowned the boy or she saw him face down in the water and did nothing to help, which was tantamount to murder.

But her defence barrister Laura Wells said she was surprised the Crown prosecutor was pursuing a murder conviction, given the expert evidence that suggests the woman was suffering an "acute schizophrenic illness" at the time of the boy's death.

"It was anticipated that (given the lay and expert witnesses to the woman's bizarre behaviour) there would be no dispute as to her mental state," Ms Wells said.

The woman spent nearly a fortnight in a psychiatric hospital following the boy's death and experts from that hospital will be giving evidence that she was "acutely mentally ill at the time the child died".

"And that she did not know the nature or quality of her actions at the time of the offence," she added.

The trial continues.