In a statement released this afternoon, her family said she worked as a caregiver for Richmond Fellowship in Christchurch and she was always helping people in need.
"As a family we are devastated that her caring nature appears to have been tragically taken advantage of," they said in a statement.
The family was shattered by her death and requested privacy and time to grieve and process what had happened.
The man police are talking to over the homicide knew the victim, police confirmed this morning.
Christchurch police investigating her death have travelled to the West Coast this morning to interview a man arrested after a vicious attack on two tourists.
Detective Inspector Tom Fitzgerald said police believed the two incidents may be connected.
Yesterday investigators identified a vehicle of interest in relation to the homicide enquiry.
That vehicle was also believed to have been involved in the attack on two tourists on the West Coast.
Mr Fitzgerald said detectives from Christchurch would be interviewing the man today and over the coming days.
The vehicle found at Woolston had been removed from the scene and secured by police, and would be forensically examined today.
A scene examination was continuing at a Woolston address where the victim lived.
Around 25 police officers are involved in the homicide probe.
At a press conference outside Christchurch central police station this morning, Mr Fitzgerald said Amy was reported missing late Saturday afternoon by a friend.
The police believe the car had been at the supermarket since around 10am Saturday morning.
Amy had spoken to people early Saturday morning, and the 38-year-old "was mentioned", Mr Fitzgerald confirmed.
He said the man was known to Amy but wouldn't confirm if they lived together, or whether he was known to police.
Police are appealing for sightings of her white Toyota Corolla and want to hear from anyone who was at the supermarket at around 10am Saturday.
"The inquiries into what her movements were are ongoing," Mr Fitzgerald said.
"It's early days. We have a number of scenes to do, and a post-mortem will be conducted in about an hour's time."
Police are not seeking anyone else.
The two female tourists were now in a stable condition in Grey Base Hospital.
The women were visited this morning by Tasman District Commander Superintendent Richard Chambers who updated them on what had occurred overnight.
"Naturally they are very relieved to know we have apprehended this man, however they are still extremely traumatised and upset after what they have been through which is entirely understandable."
He said, along with medical attention they were receiving, police were providing as much support as possible, including Victim Support and liaising with families and embassies.
Police intend to formally interview the victims once their condition had improved.
Stand-off before arrest
The man was arrested following a police pursuit and a five-hour armed stand-off after the attack on two foreign tourists on the West Coast.
The women were found on the side of the road at Franz Josef with serious injuries about 4pm.
They had been hitchhiking and were picked up at Whataroa by a man driving a blue Nissan Terrano earlier in the afternoon, Tasman District Commander Superintendent Richard Chambers said.
Police were yet to establish what happened but one of the women suffered pelvic injuries and the other had three knife wounds to the neck.
Following the attack, road blocks were put in place on State Highway 6 and a helicopter and a plane were sent to try to locate the vehicle.
It was found south of Fox Glacier shortly before 8.30pm by a police patrol.
It failed to stop and a pursuit began. The fleeing driver encountered another road block at Paringa before turning north again.
Another road block at Karangarua River, 25km south of Fox Glacier, stopped the vehicle about 9.50pm.
Armed police surrounded the vehicle and began negotiating with the man. Armed Offenders Squad members from Tasman District, Dunedin and Christchurch were also flown to the area by helicopter to assist.
The stand-off lasted more than five hours before the man was overpowered about 3am and taken into custody.
The man is being interviewed by police in Greymouth.
A 28-year-old German woman and a 27-year-old Japanese-Dutch woman are recovering at Grey Base Hospital where their conditions were described as stable.
They had spoken to police.
Police were grateful for the assistance they received from members of the public during the incident, which provided information on sightings of the vehicle, Mr Chambers said.
"It's been a long night for everyone involved, but the police staff who responded did a very professional job and as a result we had matter resolved as quickly as possible"
'I thought it was a backpack... a bag of rubbish'
The women were found by local woman Sue Hocken, who was driving through the township when she noticed a vehicle travelling towards her with its passenger door flapping open.
"I saw them being bounced out of the truck. Thrown out or jumped out, I'm not 100 per cent sure," she said last night.
"I was just driving the car and the passenger door was open on the truck that was coming towards me and then something fell out. I thought it was a backpack ... a bag of rubbish ... just something quite big.
"I thought 'something's not right', so I turned round and as I came back, he [the driver] had done a U-turn."
As the vehicle drove back past her heading towards the main road, Miss Hocken noticed two motionless women, one lying on the road, the other just off it.
She said they looked to be in their early 20s and appeared traumatised and in "major pain". One had obvious stab wounds around her throat and was bleeding heavily. The other had a deep wound to her hip and was badly grazed.
"It was pretty horrendous ... they weren't moving; they were just making noises."
One of the women was able to ask Miss Hocken to call for help, but they said little else.
Within minutes a passing tourist, who was a nurse, arrived on the scene. She was followed shortly after by the town's district nurse. The pair comforted and treated the women until the ambulance and police arrived.
The woman with the stab wounds was taken to hospital by helicopter and her companion was taken from the scene by ambulance, Miss Hocken said.
Miss Hocken, who was still feeling "quite shaky" last night, understood the women had been travelling separately but met up in Nelson and hitchhiked together from there.
- Additional reporting Otago Daily Times