An Australian police officer, who was on duty when a New Zealand mother asked for help before her two children were murdered by their father, cried in court as she apologised over what happened.

Officers found the bodies of Zaraiyah-Lily Headland, 5, and Andreas Headland, 3, on a bed inside a Yanchep home on October 20, 2016, after their mother raised the alarm to emergency services.

Their father Jason Craig Headland - who was also found at the home with self-inflicted injuries - pleaded guilty to their murders and was sentenced to life in prison, with a minimum of 31 years to be served.

Their murders were an act of revenge against his wife, Anatoria Takiwa, who had asked him for a divorce days earlier.

The children's cause of death could not be determined, but they had been drugged and asphyxiated.

The actions of police immediately before the deaths, including why it took police hours to do a welfare check, are now being investigated in the West Australian Coroners Court.

Jason Headland, father of Andreas and Zarayiah-Lily. Photo / Supplied

Counsel assisting the coroner Toby Bishop, said the children's mother, formerly of Paraparaumu, had gone to Joondalup police station to request a welfare check after she received a disturbing phone call from her estranged partner.

In the call, Headland said: "I'm going to hurt you ... I'm going to break your heart into 50 million pieces. Say goodbye to your kids. This is the last time you're going to speak to them."

Senior Constable Christine Darlington became emotional and started to cry, along with the Kiwi mother, when reading her statement in court on behalf of herself and her colleagues.

"We'd like to extend our sincerest condolences for the tragic loss of your beautiful children," she said.

"We joined police to save lives and make a difference. On this rare occasion, we were unable to do that. We too carry that burden every day. Please accept our deepest sympathy for your loss."

Darlington, who was an acting sergeant in the District Control Centre at the time, asked a recruit and a sergeant to get more information from the mother about their situation.

However, at the stage police still did not have an address to send a police officer to, she said.

Darlington said there were no reports of domestic violence involving Headland in the past and agreed with Coroner Sarah Linton's statement that police could not just assume the worst-case scenario.

As tragic as the outcome was, police acted properly in conducting their inquiries and did everything they could, she said.

On the day of their deaths, the family had been together at a medical appointment for Andreas.

Afterwards, Takiwa felt uncomfortable going home with Headland and asked to be dropped off at a train station.

As she got out of the car, he shook her hand and said: "what's done is done".

He then called her two hours later, which prompted Takiwa and her friend, Katie Cheeseman to drive to Joondalup Police Station at 6.50pm to request a welfare check.

It was the first time Takiwa had ever attended a police station and the first time police recruit Georgina Kennelly at the front counter had dealt with a welfare check request.

Three-year-old Andreas and 5-year-old Zaraiyah-Lily were drugged and smothered by their father Jason Headland. Photo / GoFundMe

"I just wanted to make sure the kids were ok," Takiwa said during the inquest on Tuesday.

"I had no thoughts of him harming the children, I just felt something was wrong ... I didn't know what.

"I didn't want him to be alone with them after that phone call."

Cheeseman said she considered Headland might kidnap the children but deep down thought he was going to harm them.

"I just knew we needed help," she testified.

Takiwa and Cheeseman both gave evidence during the inquest that Kennelly had called the children's grandparents and spoken to Headland, and that the children were okay.

"I just remember [the police] saying that the children were fine and I didn't need to go to them," Takiwa said.

"I truly believed they were with their grandparents and Jason."

After they had been at the station for about half an hour, the recruit spoke to Headland on the phone and he said he would bring the children there, the inquest heard.

But Cheeseman said she and Takiwa understood the children were with their grandparents, otherwise, they would not have left the station.

"I thought they needed to go and make sure the kids were okay," Cheeseman said. "I thought that they would do it straight away.

"I expected them to do what they're meant to do in those situations."

When Headland failed to arrive at the station, the recruit unsuccessfully tried to call him, then called Takiwa and was told Headland might be at the marital home in Yanchep, Bishop said.

The recruit created a job in the police system and gave it a priority three, which meant police were required to respond within one hour.

Officers visited the home about 10.17pm, which was just under one hour, but three and a half hours since Takiwa went to police with her concerns, Bishop said.

"By the time police officers arrived at the family home a few hours later, the children were already deceased," Bishop said in his opening address on Tuesday.

Coroner Sarah Linton will consider the reasonableness of relying on Headland saying he would bring the children to the station.

She will also examine the appropriate time police should have been dispatched to check on the children.

The inquest continues.

- additional reporting news.com.au