A Korean businesswoman laid the complaint with police which led to the sacking of Internal Affairs Minister Richard Worth, it was reported today.
The complaint, laid two weeks ago, was of a sexual nature, The New Zealand Herald said.
A friend and business associate of the complainant told the newspaper the woman was distressed.
After laying the complaint, they told a National MP's office, so that the Prime Minister John Key could be updated.
Dr Worth is a former chairman of the Korean-New Zealand Business Council, and has long links with the Korean and Indian communities.
Mr Key confirmed yesterday he knew about allegations against Dr Worth last Tuesday, but he had needed to confirm the information.
Opposition leader Phil Goff said today Mr Key should have sacked Dr Worth last week.
"The matter could have been dealt with rather more promptly," Mr Goff said.
"It was something that could have been acted on much earlier, given the other question marks around Dr Worth's judgment and behaviour."
Dr Worth announced his resignation yesterday. Mr Key said he had accepted it the previous night.
Mr Goff said yesterday he told Mr Key at the beginning of May about a complaint raised by a woman about Dr Worth's behaviour.
The complaint was not taken to the police and has nothing to do with the issue that caused Dr Worth's resignation yesterday.
"Dr Worth had offered this woman a couple of posts," Mr Goff said.
"One was as an adviser and one was as a board member within the responsibilities of Dr Worth but the overtones were that he wanted to develop a relationship with her," Mr Goff said on Radio New Zealand.
Mr Key spoke to Dr Worth and was told the allegations were unfounded.
Mr Key said last night Dr Worth should be talking with his family about whether he stayed on as an MP.
He said he would have sacked Dr Worth if the minister had not resigned.
Rumours have been swirling about the nature of the allegation against Dr Worth after Mr Key only confirmed it was for inappropriate behaviour towards a woman.
Police have confirmed they are investigating an MP for a recent incident after a complaint was laid two weeks ago.
Mr Key said there was no chance of Dr Worth getting another ministerial post, whatever the outcome of the police investigation, and depending on that Dr Worth might also have no future in the National Party, he said.
Dr Worth is the first minister to resign in the new Government, elected last November.