The Human Rights Commission has been asked to decide whether an Aboriginal group should have a say on the location of a proposed nuclear waste dump in regional South Australia.

A community vote on the proposed dump on the Eyre Peninsula was referred to the commission following accusations it discriminated against Aboriginal native title holders.

The Barngarla Determination Aboriginal Corporation last week won a Supreme Court injunction against the District Council of Kimba, postponing the postal vote which was scheduled to be sent out last Monday.

The group argued the vote of about 800 Kimba residents contravened the Racial Discrimination Act by not including native title holders.

On Thursday, the group's lawyer Daniel O'Gorman SC said the matter had been referred to the Human Rights Commission which could be a "shorter route to the finish line" than proceeding through the court.

He said he would urge the commission to give the matter urgent consideration, but he was still waiting to hear back regarding the timeline.

Outside court, Linda Dare from the Barngarla Determination Aboriginal Corporation said it was not fair her family could not have their say.

"It's depressing that we don't get to have a say over our country," she said.

"Everybody else gets to have a say — the Government and everybody else, the Kimba residents — but it's my family that's missing out.

"We don't want it. It is on our country — they can't give it to us then take it away just like that. It's not right."

Native title holders 'just want to be included'

During last week's hearing, the court heard the majority of the 211 native title holders lived outside the council's boundaries, and that excluding them from the vote had the effect of "nullifying or impairing their rights".

The group's lawyer Mr O'Gorman said his clients had no issue with the vote going ahead, they just wanted to be included in it.

"That's all they want, they just want to be included, they don't want to be treated any differently because their rights are Aboriginal rights," he said.

"There is no justification for excluding people on the basis of native title rights."

Michael Burnett, representing the District Council of Kimba, told the court the fairest manner for the council to conduct the vote was to comply with "the statutory procedure that applies in the case of elections".

"It's not a vote that has direct consequences … it's part of a range of consultations that will be taken into account," he said.

Mr Burnett said there were direct consultations taking place with native title holders about the proposed sites, a claim which Mr O'Gorman rejected.