"I hope they will interview senior police and Government ministers, including Prime Minister John Key and his deputy Bill English, about their involvement.
"Spies must be held 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 when they violate those laws."
When contacted by APNZ, Detective Superintendent Peter Read declined to comment on the investigation.
In a letter to Dr Norman, Mr Read said the Police Commissioner had directed at the beginning of October that a criminal investigation be commenced.
Mr Read said the investigation was spurred by the allegation by Dr Norman that the GCSB "acted illegally, having committed an offence ... with their involvement in the Kim Dotcom case".
"I have appointed a team of senior investigators who have assembled in Wellington and have already begun inquiries into this allegation," Mr Read said.
"In the coming weeks the team will be interviewing key witnesses in this matter before reporting to me on the outcome of those inquiries."