"Senior police and Government ministers including Prime Minister John Key and his deputy Bill English should be interviewed in order for all the facts to be established."
Mr Key has ultimate oversight of New Zealand's spy agencies including the GCSB while his deputy Mr English last month signed an order to prevent the GCSB's involvement in the case being made public.
The GCSB began intercepting Mr Dotcom's communications late last year after a request from police.
But Dr Norman said police must hold spies to the same standards as other New Zealanders.
"They are subject to the laws of this land and must be held accountable by the police and the courts if they violate those laws.
"If police find the law has been broken they should prosecute."
Dr Norman also welcomed the decision to appoint Ms McDonald to provide independent oversight, "and police also need to ensure that no one involved in the case has a say in the investigation".
But Labour Leader David Shearer said the involvement of senior police and ministers meant the investigation should not be done by police.
"This is not about scapegoating the little guys at the bottom of the food chain. It goes all the way to the top. But there's no way the police are going to be able to look into the failures of oversight and the lines of accountability that go all the way to the Prime Minister's own office."
Mr Shearer said the police were now investigating the GCSB, "thanks in no small part to the actions of the New Zealand police".
"If that's not a farce, I don't know what is."
Mr Shearer said the police investigation came on top of the "whitewash" of the Neazor report and Cabinet Secretary Rebecca Kitteridge's "secret" review.
"We don't need a piecemeal mish-mash of reviews and reports, we need a proper independent inquiry."
Key: 'They're welcome to do it'
Speaking this morning before the police announcement, Mr Key said if police chose to investigate "they're welcome to do it".
However, he yesterday questioned the need for such an investigation.
"Why would police investigate something we know has occurred? But if they want to got and do that it's up to them."
"Whether that leads to charges of any sort again that's a matter for police. They have to determine whether there's a public interest and whether there is any wrongdoing and what it is."
Mr Key said he did not agree that the police's involvement in the case - where they gave an assurance to the GCSB that Mr Dotcom and Mr van der Kolk were foreign nationals - meant they were compromised on the issue.
"They will take the complaint seriously even if I see it as a political stunt, which it is, they will take it seriously and make their own decision what they're going to do with it."