Ofsoske said the complaint was made under section 122 of the Act, which states it is an offence to print, publish or distribute material likely to influence how any person votes.
The offence carries a maximum fine of $5000. Under the Act, Ofsoske is required to pass the complaint to the police.
Hills said Danielle and Dave Grant made the complaint based on someone else sharing their voting papers on his Facebook page which showed votes for him, Chris Darby and Kaipatiki Voice.
The post has been removed by Hills from his Facebook page.
Hills said he had a call from Dave Grant "apologising and he wants to withdrawal the complaint".
"I don't know what's going on. It didn't make a lot of sense. I don't know what he is doing about it. He said he had no idea it would go this far. I don't know if he is withdrawing the complaint or what," Hills said.
When the Herald contacted Danielle Grant, she refused to comment about Hill's claim of a phone call and apology by her husband.
She issued a statement, expressing concern about a competing candidate sharing a completed ballot paper on social media and saying the matter was referred to the electoral office who in turn had referred the matter to the police.
"It is important that candidates for election play by the rules. Although the use of social media is changing the way that candidates can engage with voters, it is still important that the intent of electoral law is respected by all candidates.
"I have no further comment to make on the issues until such times as it is considered by the police," the statement said.
Said Hills: "I just think it's a distraction. I just wish people would campaign positively because this kind of stuff turns people off voting altogether. People want to hear about the issues, not politicians fighting between each other."
A police spokeswoman said that generally police do not respond to requests which seek to confirm whether specific individuals are under investigation.
"In general, if we receive information from Election Services, the general process is that the information will be assessed to ascertain whether it requires further investigation," the spokeswoman said.