"These are not the high capital crimes that Christopher Bishop has been peddling through Parliament," Jones said.
But he was concerned that confidential information had been leaked to National.
"Whose careers has he compromised accessing confidential information? This whole affair has been wracked by leaks. There have been leaks deliberately targeted and selectively accessed by Christopher Bishop and the National Party."
Bishop said Haumaha's ties to New Zealand First had been repeatedly "glossed over" by the Government.
"His candidacy for NZ First in Rotorua in 2005 was never disclosed to the Cabinet, and NZ First Leader Winston Peters has never adequately explained how he came to be at Waiteti Marae during the middle of the election campaign in 2017 to celebrate Mr Haumaha's promotion to Assistant Commissioner," he said.
Haumaha will not resign and will return to full duties as Deputy Police Commissioner in the new year.
His return follows months of working remotely while under investigation and the release of an Independent Police Conduct Authority report, which noted Haumaha had at times belittled, humiliated and intimidated staff in a way that was inappropriate and unprofessional.
But it found that Haumaha's behaviour - while heading a project across police, corrections and justice - fell short of the workplace definition of bullying, which required a persistent pattern of behaviour.
Haumaha can be fired only on advice by the Prime Minister to the Governor-General, and Jacinda Ardern took legal advice yesterday that found Haumaha had not acted poorly enough to be removed from office.