The Cook Islands Party's appeal against a High Court decision to award the Mitiaro seat to the Democratic Party will be heard at the Court of Appeal in Auckland on Thursday.
The party's lawyer, Paul Dale, says they will argue a vote should be excluded, as the voter had chosen to leave Mitiaro for medical reasons.
He says the hearing will decide how the law should be applied with regard to the validity of the vote.
Mr Dale told the Cook Islands News the hearing is in Auckland instead in Rarotonga because of the pressure from all sides to get the matters resolved quickly.
On election day last year both candidates, Tuakeu Tangatapoto of the Cook Islands Party and the island's previous MP, Tangata Vavia of the Democratic Party, got 50 votes.
But in December the High Court ruled one vote was to be deleted, giving Mr Vavia the election.
If the appeal is succcessful it could trigger the counting of votes from a by-election held in the seat following the tie on election day.