Health authorities initially blamed food poisoning for the Sarah's death, but have since said tests have proved inconclusive.
The Herald understands authorities have not yet uncovered reasons for the deaths of the three other victims - pensioners George and Eileen Everitt and local woman Waraporn Pungmahisiranon. It is not known if the authorities believe there are links.
Ms Pungmahisiranon, 47, was believed to have had an existing medical condition, but police were still waiting the results of a postmortem.
A Chiang Mai police spokesman confirmed the deaths but stressed: "It is dangerous to jump to conclusions."
Miss Carter's father Richard Carter, from the southeast Auckland suburb of Howick, said today he didn't agree with claims by the hotel's acting manager Vinai Julsiri that the deaths were a coincidence.
"I think the circumstances indicate that it's beyond coincidence," Mr Carter told NZPA.
"I'd like to see the New Zealand government push the Thai authorities for some answers, and I'd like to see the area of the hotel, if not the whole hotel, off-limits until they can come back with some conclusive results to disprove the theories floating round at the moment."
Mr Carter said his daughter had told him of the Thai woman's death when she rang to tell him of her illness, but he only heard of the English couple's death three days ago.
"I would like to see probably a thorough investigation into the rooms of the hotels because from what I understand one was beside Sarah's room, the other below it. I'd be very wary of anyone staying in or near those rooms, therefore you'd have to assume that if it was related to those rooms," he said.
"It could be anything from ... the air conditioning through to the water they've been given or food they've been served.
"It can't take too much of an investigation to work out some sort of common cause."
Yesterday, Mr Carter told the Herald he had still not been told by Thai authorities what had caused his daughter's death.
"One death the day before and two in the following days indicates it's not just pure coincidence."
The New Zealand Embassy had been helpful but had received little information from the authorities in Thailand.
Mr Carter said he hoped the New Zealand Government could apply pressure.
"We need to get answers - not so much for ourselves, but for other travellers going to Thailand."
Sarah's body did not undergo a post-mortem examination back in New Zealand.
Mr Carter said the initial shock and trauma of Sarah's death had subsided but had left behind a "constant anguish".
"We will never have Sarah with us and that's a difficult thing to live with each day.
Letters and phone calls of support had helped, he said, but each day started with the awful thought of never seeing Sarah again.
"That is a constant thing that will never leave us," Mr Carter said.
Sarah, 23, died in hospital on Waitangi Day, two days after she was found in her hotel room with friends Emma Langlands and Amanda Eliason, who were also both very ill. They have since recovered and returned to New Zealand.
Richard Langlands, Emma's father, said his daughter had only just recovered and started showing signs of her old self.
"In the last few days...she has started revisiting what happened. She is very interested now in helping to determine what happened."
The girls had been told by the hotel manager about the death of the Thai woman, he said.
Peter Eliason said the only communication from Thai health authorities had been an email asking for a new blood sample from his daughter.
"At the time (of the illnesses) we were concerned only with getting our daughter safe and getting her out. Now it is becoming very suspicious. It's all a bit too coincidental."
Mr Eliason, a farmer in New Plymouth, said tests results were promised within two weeks.
"It's way more than two weeks now and we need to have some answers."
The Herald understands the first body - that of local woman Waraporn Pungmahisiranon - was found in the room next door to the New Zealand girls either the same day or the day before the girls fell ill.
A source at the Downtown Inn said the body was covered in a sheet, and taken down a fire escape.
"They obviously took the body down that route so as to not alarm guests. It was not the easiest way out."
Less than two weeks later British couple George and Eileen Everitt, aged 78 and 73, were found dead in separate beds at their room on the fourth floor of the hotel.
Chiang Mai Police Captain Wichian Chompu said the bodies were discovered in Room 42.
"There were no signs of violence or any signs of medication indicating they might have taken their own lives," he said.
A friend of the couple, who were holidaying from their Lincolnshire home, said they had been given no indication of what had caused the deaths.
"It's knocked the stuffing out of us and we've not idea what happened," said the friend.
Hotel manager Thantep Bunkeow said he could not comment on the cause of death.
Hundreds of people have been ringing up including tour operators. I am referring all calls to police and the Department of Health."
A spokesman for the Ministry of Foreign Affairs and Trade said Thailand's Centre for Disease Control and Chiang Mai Public Health Department were carrying out investigations into the death Sarah Carter.
"New Zealand Embassy staff have requested a copy of the findings and continue to follow up with the Thai authorities.
"The Ministry of Foreign Affairs and Trade has been made aware of unconfirmed reports of the deaths of other foreign nationals in the same area and we are making contact with other Embassies in Bangkok to verify these reports."
MYSTERY DEATHS:
Feb 3: Waraporn Pungmahisiranon found dead in room 516
Feb 4: Sarah Carter found sick in room 518. She died in hospital on Feb 6
Feb 19: George and Eileen Everitt found dead in room 42
Getting back on track
Emma Langlands and Amanda Eliason have finally been able to get their lives back on track and both started back at work this week.
However, Peter Eliason said his daughter still had a long way to go.
"She can only work mornings because she gets so tired at the moment and she still has to see a cardiologist."
Amanda, who works at the Ministry for Economic Development, was in intensive care and needed a heart procedure before she was eventually allowed to fly home on February 13 - more than a week after she fell ill.
Richard Langlands said his daughter took a number of weeks to bounce back from the physical toll.
"Only in the last few days she has regained her energy and vitality. That shows you the timeframe of the impact of this."
But the emotional toll for both girls will take much longer, Mr Eliason.
"They've held it in and I don't know if it has fully hit them. Amanda has lost one of her best friends and, particularly in such circumstances, that is tough. We've all lost a lovely girl."
- additional reporting Andrew Drummond
