The new owner who sold to Kāinga Ora is reluctant to get involved in the dispute, and says he has done nothing wrong.
He told Hawke's Bay Today he simply bought the house, renovated it and made a commercial decision to ask Kāinga Ora to buy it, and they said yes.
He paid $434,000 for the home in December, and sold it in March to Kāinga Ora during level 4 lockdown for $585,000. Kāinga Ora says the purchase price was reflected by an independent valuation.
He had not lived in the home himself, but had no issues with the neighbours. He declined to comment further.
The former owners told Hawke's Bay Today they did not get on with Kāinga Ora tenants next door. They asked the Government housing department to buy their Barnett Pl, Pirimai home of 18 years, but Kāinga Ora twice said no.
Tukituki MP Lawrence Yule says Kāinga Ora's role in the transaction raises serious questions and warrants an independent investigation of its practices.
However, Kāinga Ora says there's nothing wrong with the purchase, which suited it at that particular time, and the price it paid reflected Hawke's Bay's housing market.
The couple who used to own the home now live in Hastings.
Hawke's Bay Today spoke to neighbours of the property, who told the paper that there had been no problems with the owners.
However, the couple allege verbal abuse, threatening behaviour, and say rocks and eggs were thrown on their roof.
"We decided to sell our house and move ... We felt that Housing NZ had let us down."
In July 2019, the couple approached Housing NZ through a third party and asked again if HNZ would purchase the home.
Associate Housing Minister Kris Faafoi wrote to the third party saying: "I am advised by Housing NZ that its intention is to renew and modernise its portfolio.
"Unfortunately your client's property does not meet its redevelopment plans and it will not be acquiring your client's property."
Tukituki MP Lawrence Yule said the property was one the couple would have stayed in through retirement if it were not for the neighbours.
He said it was reasonable for the couple to approach Housing NZ to purchase their property as HNZ would pay 10 per cent above the market rate and because people were aware of the issues with neighbours.
"HNZ buying would have saved real estate fees and given them a premium of 10 per cent, effectively $40,000," he said.
He said the fact Housing NZ then bought the house for a premium months later raised "big questions" about its ethics and probity.
"They [the couple] lost out by $40,000 and the taxpayer lost out by $110,000.
"This transaction needs an independent investigation and HNZ/Kāinga Ora needs to satisfy the public they are acting fairly and legally."
A Kāinga Ora spokesman said the government agency was refurbishing "fit for purpose" older homes and, on occasion, buying or leasing existing houses.
"This Napier instance is an example of Kāinga Ora buying a property," he said.
"We didn't need it at the time the couple wanted to sell. When we bought the property the situation had changed in terms of people needing homes.
"We did this on the open market at an appropriate time that matched the needs of people requiring the type of house.
"The price paid reflected the information obtained in an independent valuation. It is noted that house values in certain areas of the Hawke's Bay have continued to increase over a number of years. Kāinga Ora undertakes its own book valuations every year in June."
He said while Kāinga Ora understood a previous owner of the property had some concerns about their neighbours, the situation appeared to be mutual.
"It was the sort that is commonplace in a community where neighbours may not always get on with each other."
Faafoi said he would not comment on individual cases.