The family of a Sydney woman critically injured in a police crash are calling for the NSW Government to ban high-speed pursuits.

Key points: Gai Vieira is in a coma after a police car ploughed into her vehicle while pursuing a driver using a mobile phone

Gai Vieira is in a coma after a police car ploughed into her vehicle while pursuing a driver using a mobile phone Witnesses report hearing no police sirens in the moments before the crash

Witnesses report hearing no police sirens in the moments before the crash Her family is calling for the State Government to stop high-speed police pursuits for non-serious offences

Gai Vieira, 68, was driving her grandson Tyler when their car was t-boned by a police vehicle in Cronulla last Wednesday.

The police vehicle had been chasing a driver who was using a mobile phone.

Mrs Vieira's family alleges the police car was travelling at high speed and that she would not have seen or heard it.

"No sirens, no lights. She never stood a chance," Mrs Vieira's husband Bert said outside St George Hospital, where his wife is being treated.

"This should never have happened."

Three-year-old Tyler was sitting in the back seat and escaped injury.

However, Mrs Vieira remains in a coma with broken ribs, a punctured lung, broken pelvis, elbow and ankle, and bleeding on her brain.

"I want her back," Mr Vieira said, choking back tears.

"But I want someone to take responsibility for what's happened."

Gai Vieira was critically injured during the crash. ( ABC News )

The family is demanding the State Government follow the lead of Queensland and Victoria, which restrict police pursuits to situations in which public safety is directly at risk.

Last week a motorcyclist was seriously injured in a crash after police tried to pull him over in the harbour tunnel.

On Monday, three officers were injured when their car hit a power pole during a pursuit at Sadleir, in Sydney's south-west.

And on Wednesday, two men were taken to hospital after they crashed following a police pursuit at Berkeley Vale.

"Other states have banned all this chasing because it's cost lives," Mr Vieira said.

"It's got to stop. We've got to stop this … I'll devote my life to stopping this."

Flanked by his son Trent, daughter Cassie and extended family members, Mr Vieira criticised the lack of information coming from police.

"You have the car, you have the [black] box, you have the police officer who has a few scratches on his head," he said.

"He wiped his face down and went home to his wife.

"My wife can't come home to me."

The Vieira family is demanding to know who authorised a police chase for a mobile phone offence.

"They've told us nothing," Mr Vieira said.

"They have destroyed our family's lives."

Witness heard no sirens

The driver of the police vehicle, a male senior constable, was treated for minor injuries and later discharged from hospital.

Police have launched a critical incident investigation into the accident.

It will examine factors such as speed and whether the officer was using his lights and sirens.

Amie Bateup, who lives just metres from the crash site, was hanging out the washing in her backyard at the time of the accident and said she did not hear any sirens.

"I heard what sounded like an almighty pop, rather than a bang," she said.

"I wondered what it was and went outside because I didn't hear anything other than that sound."

"Had I heard sirens, I would have known what was going on subconsciously but there were definitely no sirens."

Premier's 'heart goes out to family'

Premier Gladys Berejiklian said her thoughts were with Mrs Vieira's family.

"I can only imagine if a loved one was the innocent victim of such an incident how we'd all feel and my heart goes out to them," she said.

However, she would not say whether she believed the rules surrounding police pursuits should be changed, because she did not want to pre-empt the investigation.

"I want to assure them and the community that police aren't leaving a stone unturned in relation to investigating the matter," she said.

"If there's anything the police need to do or there's broader issues of course we'll address them."