Ms Burch's former chief of staff, Maria Hawthorne, resigned in December amid allegations she disclosed conversations between her boss and Chief Police Officer Rudi Lammers, in a scandal that also ended the ministerial career of Ms Burch.

The affair saw a scrappy start to the first Assembly sitting day for the election year, as the opposition attempted to block Ms Burch from committee positions.

Police have focused on a conversation she had with Dean Hall, the ACT Construction, Forestry, Mining and Energy Union boss, in April. Last week, Fairfax Media revealed a list of 11 questions police put to Ms Hawthorne through her lawyer.

The affair remains largely unexplained, with both Mr Barr and his deputy, Simon Corbell, insisting in December that the allegations against Ms Hawthorne were serious and unprecedented, warranting her departure, and Ms Burch's departure from the frontbench, taking responsibility for the actions of her office.

The police questions focused on whether Ms Hawthorne held national security clearance while working for Ms Burch and what contact she had with Mr Hall, especially in April last year when Mr Hall was under investigation by the trade unions royal commission and his phone was widely believed to have been tapped by investigators.

The questions suggest police are focused largely on what she told Mr Hall in that conversation, but Mr Barr and Mr Corbell have both continued to insist that the investigation goes beyond the relationship with Mr Hall and the April phone call.

This week, Mr Corbell, who is now Police Minister, stood by his comments.

"Absolutely I maintain that position because that is the advice provided to me by ACT Policing," he said, but he could not comment on specifics, nor on the nature of the investigation.

"I maintain that this is a serious matter, It is quite unprecedented for there to be a police investigation into these circumstances, the day-to-day functions of a minister's office, so I stand by those comments as well."

Asked this week whether he maintained confidence in the police investigation, Mr Barr said "yes". Asked whether he was confident other conversations from inside the government hadn't been recorded by police, he said he had "no reason to think otherwise".

Police have refused to comment on the progress of their investigation and on the questions they put to Ms Hawthorne. A spokesman said work was not yet complete and it was "therefore inappropriate for [police] to comment any further".

Police also confirmed they are not investigating the leak to Fairfax Media of the police's concerns about Ms Burch's office.While the federal police, of which ACT Policing is a part, is responsible for investigating disclosures of confidential government information, which is a criminal offence, a spokesman said police were not investigating.

Earlier on Tuesday, Liberal Leader Jeremy Hanson tried to block Ms Burch from heading committees, saying members in positions of authority must have the confidence of the Assembly and the community.

"My very firm view, and the view of my colleagues, is that Ms Burch should not be elevated to the position of chair or deputy chair, this is about taking the committee system and appointment in this Assembly seriously," he said.

Ms Burch is now one of only two Labor backbenchers, with the second, Mary Porter, retiring at the end of next week. The shortage of backbenchers leaves Ms Burch and newcomer Jayson Hinder, who is expected to take Ms Porter's seat on a countback of votes, representing Labor on all of the Assembly committees, including as chairperson or deputy chairperson.

Until the Assembly knew precisely what Ms Burch's office is alleged to have done, it would be "reckless" to put her in a position of authority, Mr Hanson said.

"It is extraordinary what we are being asked to do," he said.

But Mr Barr said there was no police investigation into Ms Burch herself.

"The assertions ... to Ms Burch that she needs to be exonerated are a fundamental mis-statement," he said.

"There is no reason … why Ms Burch cannot serve in the committee system in this place. We have 17 members. The suggestion is that a sole non-executive Labor member will be simultaneously chair, deputy chair, and [be a] member of all committees is a ridiculous proposition."