Labor and the Greens fired questions at the Premier over why he continued to stand by the Braddon candidate amid allegations he had dated two women under a false identity and was facing firearms charges by police.

Labor leader David O'Byrne asked Mr Gutwein why he believed Mr Brooks was a fit and proper candidate for Parliament.

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Mr Gutwein replied that he had no dealings with Mr Brooks to suggest otherwise.

"With the allegations that were raised, he proclaimed his innocence every step of the way," he said.

"In terms of Mr Brooks, I will make this point: I wish him well. He is unwell - there are no two ways about that."

Greens leader Cassy O'Connor asked if Mr Gutwein would apologise to the women involved for believing Mr Brooks' version of events over their own.

Mr Gutwein said:

"Regarding women who have anonymously made complaints about Mr Brooks, if those matters are found to be true then that is a very unfortunate set of circumstances they find themselves in."

Mr Gutwein denied he continued to defend Mr Brooks because he was a Liberal Party donor.

After Question Time, Mr O'Byrne said Mr Gutwein stood by Mr Brooks day after day after allegations were raised and even labelled his candidate cabinet material.

"It's no longer about Mr Brooks - he deserves procedural fairness, he deserves his time in court - this is about Mr Gutwein and the decisions he chose to seek power in this Parliament," he said.

The Greens on Wednesday tabled to bill to close a loophole in legislation governing the Integrity Commission which prevented a member of Parliament from being investigated for actions undertaken during an election campaign.

The party had referred Mr Gutwein's handling of the Adam Brooks affair to the commission which in turn informed them it did not have the legislative authority to undertake an investigation.

Ms O'Connor said the bill would ensure a sitting member of Parliament remained a member of Parliament under the act between the vacation of their seat and nomination day.

If that person was to recontest the election, they would be a member of Parliament under the act between nomination day and polling day.

"While it is true a member of Parliament is not considered a member during an election period, they retain benefits of the office," Ms O'Connor said. "These benefits include staffing and resources, a parliamentary salary and general influence."