The complainant said the statement was false, as none of the candidates lived in Invercargill, and any of the candidates would retain the number of MPs for Northland.
The flier was referring to the possibility of Winston Peters bringing an Invercargill list MP into parliament with him.
The Authority chairman said the flier was the candidate's interpretation of the impact on representation for Northland if he was not elected.
The issues in the flier were the subject of considerable public debate, and there was no apparent breach of the code of ethics.
Election ads supporting Mr Peters have also come under fire. Ads by Focus NZ candidate Joe Carr, which urged voters to support Mr Peters, did not have his written permission, as required by the Electoral Act.
In the last week of the campaign Focus NZ candidate Joe Carr ran two front-page advertisements in the Northland Age urging voters to "vote for Peters" and at least one in the Northern Advocate. The two Northland Age ads ran next to Mr Peters' own campaign ads.
Under electoral law, anyone promoting a candidate in an election advertisement needs the candidate's written authorisation to do so.
Mr Peters said he was grateful for Mr Carr's support but had not authorised the ads nor had he known about them; Mr Carr confirmed he had not approached Mr Peters for permission and did not realise he should have.
The Electoral Commission said if the advertisement was published without the authorisation of the candidate the advertiser could be in breach of the Electoral Act.
Asked about Mr Carr's advertisements, a spokeswoman for the commission said it would wait to see what was declared in the candidates' returns before deciding whether to take action.
"If prosecuted, it is an illegal practice and carries a fine of up to $40,000 because Mr Carr was a candidate. If he was not, the fine would be up to $10000."
Otago University electoral law specialist Andrew Geddis said in theory illegal practices could be grounds for an election petition to overturn the result if they had a significant enough effect on the outcome.
"I very, very much doubt a couple of newspaper ads from a fringe candidate would suffice here."
If Mr Peters had authorised it, he would have to include some of the cost of the ads in his own expenses. Candidates can spend $26,100 on their campaigns in a general election but about double that ($52,100) in a byelection.
If an advertisement promotes two candidates, both are expected to split the cost in their return.
Mr Peters said he was well under the spending cap.
Mr Carr was one of several byelection candidates who supported tactical voting for Mr Peters in the campaign. He is not alone in coming to the Electoral Commission's attention for those efforts.
The Electoral Commission is also looking into a placard carried by Independent candidate Bruce Rogan which urged people to vote for Mr Peters but had no authorising statement on it. Mr Rogan was seen carrying the home-made placard when the Prime Minister was in Dargaville last Thursday. The Electoral Commission said it needed an authorising statement from Mr Rogan and Mr Peters' written authorisation.
Meanwhile, Mr Peters' success in Northland will result in a boost in funding of about $360,000 a year for him and his party. That includes $91,731 in extra funding Mr Peters gets as an electorate rather than a list MP and $179,400 the new list MP will qualify for. That funding is largely to run offices and pay staff.
NZ First will also get $86,320 more in party and leader's office funding when its caucus goes from 11 to 12 MPs. Mr Peters' salary will increase by $1290 because of the extra MP, as will party whip's Barbara Stewart.
-additional reporting NZME. News Service staff
