Six months after Metiria Turei revealed her historic benefit fraud, neither she nor the Ministry of Social Development are commenting on the case – including whether the former MP has repaid the debt.

MSD launched an investigation in August after Turei - then the Green Party co-leader - said that she had received benefit payments she wasn't legally entitled to while studying law as a solo mother in the 1990s.

Turei, who said she had mislead welfare staff about her living situation, made the revealation while she and current sole party leader James Shaw were announcing Green Party policies of increasing benefits and abolishing penalties for beneficiaries.

Six months on and neither Turei - who later stood down as co-leader and wasn't re-elected at the election - or MSD are commenting.

Turei - who has previously said she would pay back any money she owed - didn't respond to messages left by the Herald on Sunday and a spokeswoman for the Ministry of Social Development said it "will not and cannot" comment on individual cases.

But critics say they are concerned there was a lack of transparency around the subsequent MSD investigation.

New Zealand Taxpayers' Union director Jordan Williams says the ministry is "stonewalling" the public, while Act leader David Seymour has queried why the inquiry is taking so long.

Seymour said "there should be an investigation which is on an equal basis to which any other beneficiary should expect" and queried why it was taking so long.

The revelations had backfired on Turei, he said, and she had let down her own voters.

"The reality is, the most incensed people were single mums on a benefit."

Williams said too many questions remained unanswered.

"The public is entitled to know and expect that laws that apply to them apply to MPs and former MPs. If ever there is a case where the public deserve information this is it," he said.

He said the Ministry was "stonewalling" the public.

"Justice not only has to be done it has to be seen to be done. She said she would pay it back - well, why is it so difficult to say it's been done?"

The former MP resigned as co-leader weeks after the controversial speech where she admitted lying to Work and Income in the 1990s.

She initially refused to resign but left the leadership weeks later blaming the "unbearable" public scrutiny of her family.

After the meeting she said she was unsure whether she would be prosecuted, but had no regrets.

"We have had a national conversation about what welfare is like, how hard it is, how impossible it is for people to live well and that we need a more compassionate and caring welfare system, not one that penalises people," she said at the time.

Former Green Party member David Clendon, who along with Kennedy Graham resigned in protest at Turei's actions, told the Herald there was a fine balance between the public interest and Turei's privacy.

"I would expect there would be some sort of information that would come into the public domain if for no other reason than to retain the integrity of the system. Obviously there's a huge public interest."

Turei attended Greens campaign events in Otara in September but lost the Te Tai Tonga electorate. She was reported saying at the time she would always be in politics- just not in Parliament. In November she tweeted to a supporter she was "still around, just enjoying the quiet".

National's social development spokeswoman Louise Upston said the investigation wasn't a priority for her and she hadn't asked questions about it. "It's not really an area of interest for me."

Shaw declined to comment through a party spokesperson.

TIMELINE

July 16, 2017: At a Green Party Mending the Safety Net policy launch which they promised would reform the welfare system Turei said she had a "responsibility to tell it how it is", admitting she had made misleading claims about having flatmates while a beneficiary.

August 3, 2017: Turei met with Ministry of Social Development investigators but told reporters afterward she had "no regrets" about her admissions.

August 7, 2017: Senior Green Party MPs Kennedy Graham and David Clendon resign in protest at Turei's actions but co-leader James Shaw continued to back Turei.

August 9, 2017: Turei resigns while polls showed the Greens slumping.