And there are now calls from many upper-house senators for the constitution to be changed after yet another politician has come under the spotlight over citizenship.
Just days after Queensland senator Matt Canavan resigned as federal-resources minister over his citizenship issues, fellow senator Malcolm Roberts is now facing strong scrutiny.
The One Nation senator, born in India to a Welsh father and Australian mother, insists he took all reasonable steps to renounce his British citizenship.
And he claims he received a confirmation letter months after his election.
Senator Roberts has told Sky News he wrote to the British consulate several times before signing his nomination form to stand as a One Nation candidate.
"I wrote again, again and again to the British and said, 'I believe I am not a British citizen, and, just in case, though, if I am, then I renounce it.'"
He says it was not until December last year he received a response confirming he is not a British citizen, but he will not publicly release the documents.
"I didn't want to release the documents, because you see what the Twitter-rati* do. They just misrepresent some of these things. We've seen that already with other people. I could see that they'd be doing the same with me."
Questions were raised about his citizenship after Buzzfeed News published an article showing the Senator had travelled on a British passport when he was a baby.
One Nation leader Pauline Hanson says she is confident Senator Roberts is not a dual citizen.
She says she witnessed him renouncing his British citizenship before he became a candidate last year.
Defence-industry minister Christopher Pyne has told the Nine Network he believes the High Court needs to clarify section 44 of the constitution.
The section says people are disqualified if, at the time of an election, they are a citizen of "a foreign power" or have an "allegiance, obedience or adherence to a foreign power."
Mr Pyne defended the recent controversy surrounding Senator Canavan with an unusual North Korea comparison.
"On that basis, Kim Jong-un can make us all citizens of North Korea and we'd all have to resign ... (laughs) ... There's got to be some rules. You can't just make me a citizen of another country without me knowing it and then, apparently, I have to resign from the House of Representatives. I mean, there's got to be some common sense."
Appearing on the same show, Labor MP Anthony Albanese said he was confident the Labor Party would not fall victim to the citizenship scandal.
"When we nominate for parliament, you have to produce evidence, your birth certificate -- if you're born in another country, you have to produce evidence that you've renounced citizenship. We check these things out. We've checked out all our people. All our people are fine."
Greens leader Richard Di Natale says he is not a fan of the current citizenship restrictions.
He says he thinks the constitution should be amended to reflect the nation's diverse society.
"Look, it's a relic of the past, okay? Let's be frank about it. But it's a constitution, it's our founding document, and it defines who's eligible to stand for parliament. It goes to the heart of what our democracy looks like, and you can't pick and choose this stuff when it comes to the constitution. So, the Government's got a wafer-thin majority, it doesn't want to open this up to scrutiny. It's more interested in protecting its own Members of Parliament than it is in upholding the constitution."
