Police knew a Wellington mother charged with the manslaughter of a baby who drowned in the bath threatened to gas her children - but the jury was not told.

The mother made the statement two weeks before her 13-month-old son drowned unattended in a bath. But according to the baby's distraught father, police failed to interview a potential witness who heard the statement.

The mother - who cannot be identified - was acquitted in the High Court at Wellington late last month. She pleaded not guilty to the manslaughter of the boy, who drowned last November while she spoke on the phone for about eight minutes.

The baby's father had split up with the mother - who had mental health issues - just two weeks before their son's death.

Police insist they considered all the evidence, but say some was not relevant.

But a Dominion Post investigation into the background of the trial has revealed disturbing evidence the jury did not hear, including:

- The baby's father told police in a formal witness statement that the mother repeatedly left another baby unattended in an upstairs bath.

- The mother had a history of drug and alcohol abuse, was known to Child, Youth and Family, and had left her children unattended in a car as she shopped.

- Another witness said the mother twice threatened to make the father of the baby "regret it" if he left her again.

That witness rescued another child of the mother's as he was unattended and running naked outside near a motorway.

The mother admitted giving marijuana to her daughter, aged under 10, and would drive drunk with her children.

She sent a text saying she was responsible for the drowning and would plead guilty.

It has also emerged that her father is a police manager and her mother works for police on occasions. Both gave evidence for the Crown.

In a police video interview played to the jury, the baby's mother said she had never left her youngest child unattended in the bath before.

But in a 33-page statement - which the jury did not see - the baby's father said she repeatedly left another child aged about 2 unattended in a bath.

"I'm amazed she got off," he told The Dominion Post.

His statement reveals numerous examples of difficulties his former partner had with parenting skills, and their rocky relationship.

He said police were given "a lot of stuff that the jury were not allowed to hear that I thought would be crucial to the case".

The mother's father said the death of his grandson and the manslaughter charge was devastating for his family, and he was concerned risks remained for his other grandchildren as, since the drowning, some people had expressed anger and threatened his daughter.

"It is clear many people have no tolerance for any lapse by parents in their attention to children in and around water.

"I hope the bitterness our daughter's enemies feel will in time abate. Not only to reduce the risks to my family, but so that they can get on with their lives as well."

He said he was pleased with how his daughter had been raising her youngest and she'd done many positive things for him.

Police said the Crown was told of the alleged threat about the mother gassing her children, but it was deemed not to be relevant.

Detective Senior Sergeant Mike Oxnam said he was confident the facts presented to the jury represented what happened to the baby, and the inquiry was thorough and comprehensive.

The baby's father said police told him he was not needed as a witness because they were focusing on the events of the day.

His statement said his former partner smoked cannabis most days, sometimes in front of her children. "If she ran out of weed when she was drinking, [she] would drink-drive and go and get some more."

After his former partner walked free, he was contacted by a potential witness who said police were told during the trial about her threatening to gas herself and her children, but failed to reply to messages.

Another witness described in a 17-page police statement how she once turned up at the mother's house around lunchtime to find her drunk, with a naked child running towards bush leading to a motorway.

It was "chilling" to be told by the mother that day that her partner would "live to regret it" if he left.

The mother repeated the threat about two weeks before the baby drowned, she told police.

"I think the jury should have heard all that and, if there had been no name suppression, I believe others would have come forward," she said.