National leader Simon Bridges says the inquiry the Government is setting up into the appointment of the Deputy Police Commissioner is unsatisfactory and Tracey Martin should not oversee it.
He said it should be broad enough to include whether proper disclosures were made to the cabinet about Haumaha's former association with New Zealand First.
Tracey Martin, the Minister of Internal Affairs, was a senior New Zealand First official and it was inappropriate that she be involved.
"I think this is incredibly serious," said Bridges. "Winston Peters has serious questions to answer to ensure that we can all have confidence in the police and they are not being politicised."
Acting Prime Minister and New Zealand First leader Winston Peters announced a broad outline of the inquiry to be set up by his colleague.
It will look at whether all relevant information was given to or gathered by the State Services commission during the appointment in May, if it was, whether all relevant information was provided to ministers.
Peters said Tracey Martin would release the terms of reference and name a suitably qualified independent person to conduct the Government inquiry.
He said he saw no reason why the report would not be made public.
The Cabinet Manual says a Government inquiry usually deals with issues whether a quick and authoritative answer is required from an independent inquirer.
The announcement of the inquiry followed revelations in the Herald last about comments Haumaha had made in Operation Austin which investigated rape allegations made by Louis Nicholas. She was furious about his latest promotion.
Haumaha issued a statement on Friday acknowledging his comments but unreservedly apologised for them and said they did not reflect his values today.
Rotorua Daily Post archives from August 2005 show that Haumaha was announced as the New Zealand First candidate at a meet-the-candidates event in Rotorua. A short time later Fletcher Tabuteau, now the party's deputy leader, was named as the candidate.
It emerged the followed month, after a suppression order against Haumaha's wife was lifted, that she had gambled away money set aside for his 2005 campaign.
According the Post's report of the court case, she had stolen about $24,000 from the bank where she worked to replace the missing campaign funds.
Haumaha had been an Inspector at the time.
Peters said Tracey Martin had been chosen to oversee the inquiry because you couldn't have the Minister of Police of the Minister for State Services - the appointment panel comprised the Commissioner of Police, the State Services Commissioner, and the Deputy State Services Commissioner.
Peters rejected a suggestion Martin was compromised because she was a New Zealand First MP.
"She is not only a New Zealand First MP, she is a cabinet minister well aware of her responsibilities."
Peters acknowledged that Haumaha had pulled out of the candidate process "but a whole lot of people start and stop."
"I can recall [former Prime Minister] Geoffrey Palmer left the National Party to join the Labour Party and become the candidate for Christchurch Central a long time ago. No one thought he was compromised."
Palmer was a law lecturer at the time.
She is not only a New Zealand First MP, she is a cabinet minister well aware of her responsibilities.
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Bridges said that Tracey Martin should not be allowed to oversee the inquiry and that the inquiry should also look at any disclosures to the cabinet about his former links to New Zealand First.
Bridges: "I believe we have now gone past this simply being about Operation Austin and what Wally Haumaha has said there because more has come out which means there are serious questions about Wally Haumaha's political affiliations and what role that has played in his appointment as Deputy Police Commissioner."
Peters dismissed Bridges' suggestion that he should have told the cabinet about Haumaha's former bid to stand for New Zealand First.
"A lot of people seek election and selections all over the country. That does not bind them years and years later like 13 years later, surely, otherwise we are going to have some kind of secret society here dominating peoples' professional outcomes and that would be unfair."
Peters did not believe it was necessary for Haumaha to stand aside while the inquiry went one.
Bridges said he was less concerned about Haumaha himself and more concerned about whether proper processes had been followed.