'I won't be commenting': Rockliff grilled after Ogilvie resigns as minister

Madeleine Ogilvie resigned from her cabinet position on Saturday, relinquishing her ministerial portfolios. (ABC News: Ebony ten Broeke)

Budget estimates hearings started in Hobart today, with Premier Jeremy Rockliff facing a grilling from both Labor and the Greens to reveal more details of ex-minister Madeleine Ogilvie's Supreme Court legal fees.

Ms Ogilvie resigned as a minister on Saturday and will now sit on the backbench after she was accused of misleading parliament over whether she was party to any Supreme Court proceedings.

A political analyst says three former ministers are likely the frontrunners to be promoted to cabinet (Michael Ferguson, Roger Jaensch and Mark Shelton) with an announcement expected this week.

Tasmanian Premier Jeremy Rockliff has refused to provide any information about cabinet's decision to pay for Liberal MP Madeleine Ogilvie's legal fees, on the basis of legal confidentiality.

Ms Ogilvie was accused of misleading parliament after she first told an estimates committee in November that she was not a party to any Supreme Court proceedings, but then last week revealed in parliament she was in fact involved in Supreme Court matters she initiated.

She resigned as a minister on Saturday evening, saying she did not want the government to be "distracted by this matter".

But the Greens — who asked the question that started the saga — and Labor say the premier has questions to answer, like what he knew and when.

In estimates on Monday, the premier was repeatedly asked questions by the leaders of both parties, but he offered little beyond the fact the matters were complex, "particularly given the confidentiality requirements".

He also said Ms Ogilvie would reveal the full details when she could.

Labor leader Josh Willie: When did you authorise Supreme Court proceedings? You would've had to approve it.

Mr Willie: This is about what you knew … this is about you and what you knew at what time.

Premier Jeremy Rockliff faces questioning during a committee hearing on Monday. (Supplied: Tasmanian Parliament)

Mr Willie also asked Mr Rockliff about the state's Integrity Commission.

"If the Integrity Commission completed an investigation and a person named in the report commenced Supreme Court proceedings challenging the process or findings, would that prevent the commission from publishing the report?"

Tasmanian government minister Madeleine Ogilvie will move to the backbench after accusations she misled parliament.

The premier was given no reprieve from Greens leader Rosalie Woodruff, who was trying to find out if the legal m