Tasmanian Labor MP Justine Keay has dismissed calls for her citizenship status to be referred to the High Court as "stupid".

Ms Keay was still a British citizen on election night last year, but argued she took all reasonable steps to renounce her dual allegiance.

Tasmanian Liberal power broker Eric Abetz is on her case, pushing for her eligibility to be tested by the High Court.

Senator Abetz said he believed Ms Keay was ineligible.

If the High Court agreed it would force a by-election in Braddon.

Ms Keay showed Fairfax Media documents proving her claims but has not released them publicly.

"I'm not going to refer myself, I can't — the Parliament needs to," Ms Keay told ABC Radio Hobart.

"I've received a lot of legal advice that clears me.

"There is no doubt. It would just be stupid for me to be referred to the High Court."

But that was not good enough for Senator Abetz.

"Ms Keay should be referred to the High Court and if, as Labor keeps saying, she is confident in her legal advice, then Ms Keay has nothing to worry about," he said.

"It is deeply disappointing that while Coalition MPs, and even Senator Lambie, have acted in an honourable way by being fully transparent, Ms Keay has had to be forced out."

Ms Keay said she would participate fully in whatever parliamentary process to determine the status of MPs was decided on.

Likening Turnbull to dictator 'sad nonsense'

Prime Minister Malcolm Turnbull and Opposition Leader Bill Shorten are exchanging letters on how and when MPs should prove their citizenship status.

Mr Turnbull has said if a process could not be agreed on, all cases in doubt should go to the High Court.

Ms Keay said that was bully behaviour.

"If Malcolm Turnbull is threatening to refer his political opponents to the High Court then that's the stuff of a desperate tin-pot dictator," Ms Keay said.

"I will release my documents publicly through a parliamentary process.

"I have absolutely nothing to hide and I have been cleared time and time again."

Ms Keay said the process should be "robust and transparent".

"We need to instil confidence back to the Parliament."

Senator Abetz said Ms Keay's comments were nonsense.

"To try to suggest that Malcolm Turnbull referring her and others to the High Court is like a tin-pot dictator is just sad nonsense and obfuscation when you realise that Malcolm Turnbull voted to refer Barnaby Joyce, his very own deputy Prime Minister, to the High Court to have this resolved," he said.