William Tyrrell’s biological mother has told a coroner of the day in 2014 that police arrived on her doorstep after the three-year-old disappeared and asked if he was there.

“They didn’t tell me anything … they looked around … they asked what I’d done, blah, blah, blah, and left,” the woman testified at the NSW Coroners Court on Thursday.

The mother, who can’t be identified for legal reasons, said she stood by her statement to police that she “didn’t take him” and “definitely” doesn’t know where William is.

In that document, the woman states: “If I took him, I would be gone and I would have [his sister] as well. I want a normal life. I don’t want to be hiding away with them somewhere.”

Her last supervised contact visit with her son was on August 21, 2014.

William vanished while playing in the garden of his foster grandmother’s Kendall property on the NSW mid-north coast on September 12 that year.

His biological father testified on Thursday at the inquest into the boy’s disappearance and suspected death.

The man said he was at home in Sydney when he found out William was missing.

Junior counsel assisting the coroner, Tracey Stevens, asked: “If you were informed by anyone of information of William’s whereabouts, what would you do?”

“I’m still waiting to be informed,” the man replied.

When questioned about the involvement of authorities, including the Department of Family and Community Services, he said: “They f—ed up.”

“It was the minister’s duty of care to keep him safe until he was 18 and that was not the case at all. FACS was about keeping kids safe,” the father said.

Both parents conceded they “absconded” with William and hid him for five to six weeks in early 2012, after a children’s court determined he was a ward of the state.

The mother said she was aware of adoption plans before he disappeared but not in any detail.

The father told the court: “Through everything that happened, I really had no regard for any of that controversy. It was just something … in one ear and out the other.”

Senior counsel assisting the coroner, Gerard Craddock SC, told the inquest the police investigation was ongoing.

“We certainly haven’t given up,” he said.

“If anybody, either in the room or in the community generally has any further information which they think might be of assistance … we want to hear from them.”

A directions hearing will be held on April 24 ahead of a month of hearings in August when persons of interest will be called to give evidence.

-AAP