National has complained to the Auditor-General over what is says are issues in the way the Government has handled the potential closure of partnership schools.
National's spokeswoman for Education, Nikki Kaye, said she sent a letter to the Auditor-General outlining a concern over perceived conflicts of interest.
The complaint also touches on what she called several "unfortunate comments" made by Education Minister Chris Hipkins about the issue.
"I want to stress that while I believe there are serious grounds for the Auditor-General to investigate, it will be up to the Auditor-General to determine if there have been any issues with the process regarding partnership schools and any potential perceived conflicts of interest," she said.
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"It is important that all the evidence and paperwork is made available and transparent before any conclusions are reached."
Earlier this month, Hipkins announced the Education Amendment Bill, which would end National's "charter school experiments".
Charter schools were driven by ideology rather than evidence, he said, and the Government believed there was no place for them in New Zealand education.
Kaye pointed to comments made by Hipkins in recent weeks about partnership schools.
She said they indicated he had a "closed mind" and there was therefore potential evidence that the schools involved were being pressured to terminate their contracts.
"I believe the minister's and the ministry's process is fundamentally flawed and there is public interest in investigating it."
The letter also touched on a potential failure of ministers to manage or declare conflicts of interest.