The review was ordered in the light of revelations of supportive comments he made about former friends who were accused in 2004 of the rape of Louise Nicholas, for which he has apologised.
But National has also said that Haumaha's close links to New Zealand First MPs should have been declared to the cabinet before it decided.
National deputy leader Paula Bennett took exception to Shane Jones' objections in the House: "As one of those Māori there is actually also a convention that we express our conflicts of interest for whānau and particularly when we are looking at making statutory appointment and this side of the House has a right to question that."
Peters spoke at a marae celebration for Haumaha's promotion last year to Assistant Commissioner but insists that the police asked him. Tabuteau mentioned Haumaha as whānau in his maiden statement.
Tabuteau is a member of the executive as an under-secretary although not a member of the cabinet which signed off on the Deputy's appointment in May.
Bishop told the Herald later there was an implication was that he was being racist by raising the family connection.
"There are links between various members of New Zealand First and Mr Haumaha," Bishop said.
"It is an extremely important office that he has been appointed to and we are doing our job as responsible members of the Opposition in investigating whether or not the appointment of Mr Haumaha has integrity."
Jones' objections came after Bishop asked Prime Minister Jacinda Ardern if she had confidence in the professional independence from Mr Haumaha "when her Police Minister gives him a shout-out in his workout videos, her Deputy Prime Minister [Peters] attended a celebration on a marae for his appointment as Assistant Commissioner, her Foreign Affairs under-secretary has whanau links to him and he was previously announced as a candidate for New Zealand First?"
Peters said outside the House that Bishop was talking about "a tissue of lies."