The inquiries include a police homicide investigation, an internal police policy, practice and procedures review and an Independent Police Conduct inquisition.
Ms Venables said no one else other than the man was being sought in relation to the death at a property on The Esplanade on the Westshore beachfront, thought to have happened about 9pm on Monday. She said a pursuit started after police were told of a man with a firearm driving south out of Napier and road spikes were put in place near Clive.
Clive resident Ray Beale said he became aware of the chase on Facebook. He soon heard the vehicle approaching the riverside township - the sound making it "obvious" it was running on its rims, presumably after hitting police road spikes.
"Then it stopped," he said. "I only heard five shots. There was one shot, and then four others."
He drove around to the scene but was stopped by a police officer about 100m from where the shot man was apparently on the side of the road.
Casey Mikaera lives about 15 houses down from the shooting.
She too was woken by a car speeding by, with police in hot pursuit. She did not hear any shots though.
"We were in bed and I heard what sounded like a tank. I thought it must have been a tsunami as we are close to the water," she said.
"It was quite late and I didn't know how anybody couldn't have heard that."
Miss Mikaera sleeps with her curtains open so had a look out the window. "I saw two AOS vans driving past and then a number of police cars."
About 10 minutes later she went outside and heard people from the nearby hotel talk about how there had been a shot fired.
While an early police release said the man was shot by police, at the conference Ms Venables would not confirm the nature of the man's injuries, although she said officers immediately applied first aid at the scene in Clive, near the intersection of State Highway 2 and Mill Rd.
Declining to answer several questions during the conference, she did not disclose identities of the woman and the man, their relationship or whether any children were at the Westshore address when the woman died. The woman has a 5-year-old daughter.
Ms Venables said police were seeking any information which could be linked, including the movements of the man and the dark red Toyota Corolla saloon he was driving, between about 8.30pm and 11.10pm when the events came to an end.
She would not reveal whether any suspect weapon had been found by police,
The incident in Clive closed a significant stretch of State Highway 2 for most of the day as police began investigations. Main highway traffic was rerouted.
In Westshore on The Esplanade, residents around the unit where the woman died were visibly distressed by what had happened.
Asked if she knew the couple, one woman nodded but said she did not want to talk about it.
A resident of one of the four units on the property said she heard noises but did not want to say anything else.
A close neighbour said they needed time to themselves, to take in what had happened.
The middle unit where the incident took place had a basketball hoop beside one wall and there appeared to be children's playthings nearby.
While police and forensics investigators focused on the property and the shooting scene in Clive, they also searched roadsides.
'She was kind, beautiful'
The young mother found dead in her Westshore home has been described by friends as the "strongest, kindest and most beautiful person" they had ever met.
Friends and family were mourning the death of Victoria Foster, 24.
A 28-year-old man shot after a police chase has been linked to her death. He remained in a serious but stable condition in Hawke's Bay Hospital last night.
Sarah Paroli, Sarah Howes and Renee Hunt said they were still in shock at the news of their friend's death.
"It hasn't quite sunk in yet," Ms Paroli said.
There was nothing they could not tell Ms Foster. "She would never judge us, she was a huge part of our lives."
Ms Paroli met the mother at a baby playgroup. Miss Foster's daughter was now 5.
A Napier principal said the woman was one of many "lovely" parents - "as was the father".
Her daughter's school was told of the incident by Victim Support yesterday morning, and the girl had not been at school during the day. "She's a lovely child, never puts a foot out of place," the principal said.
Ms Paroli said her friend was hard-working and an "amazing" person.
The Plunket nurse had recently landed her "dream job".
"She loved it. She took a part of us with her and we will miss her every day."
Another young woman who spent her high school years in the same form class as Ms Foster and attended her intermediate has spoken of a kind natured person. "She was such a nice girl and an awesome young mother. She had a lot going for her," she said.
