The minister says doing so could have jeopardised an ongoing police investigation and it was "completely irresponsible" to suggest otherwise.

Appearing before a budget estimates committee today, Mr Shelton was grilled on his knowledge of the police investigation into Mr Griffin, who died at age 69 in October 2019, after being charged with numerous offences relating to the repeated sexual abuse of a child.

The hearing followed Premier Peter Gutwein's announcement on Monday of a commission of inquiry that would look into historical allegations of serious sexual abuse of children in government institutions, including public hospitals, state schools and the Ashley Youth Detention Centre.

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Deputy Labor leader Michelle O'Byrne asked Mr Shelton when he first learnt of Tasmania Police's investigation into Mr Griffin, who worked on the children's ward at the Launceston General Hospital for close to two decades, as well as briefly at the Ashley Youth Detention Centre and providing ambulance services on the Spirit of Tasmania ferries.

"Can I ask if you discussed this issue formally or informally with the relevant portfolio ministers or the premier?" she said.

"Late August [2019] was when I acknowledge I was verbally informed," Mr Shelton said.

When Ms O'Byrne pressed Mr Shelton to answer the question, he conceded he hadn't informed the relevant stakeholder ministers.

"As you would be aware, the Premier has announced this [commission of inquiry] and, of course, it would be inappropriate for me to talk about specifics of individual cases," he said. "It was an ongoing police investigation at the time and, therefore, it was not appropriate for me to comment."

Human Services Minister Roger Jaensch and Education Minister Jeremy Rockliff oversee agencies in which the late Mr Griffin was involved at one time or another, yet both learned of the allegations through the media.

Meanwhile, Health Minister Sarah Courtney confirmed earlier this week in a separate budget estimates hearing that she had first learned of the allegations on July 31 last year, when Mr Griffin's working with vulnerable people registration was revoked.

A complaint about Mr Griffin, formerly of Legana, was first made to Tasmania Police on May 1, 2019. Child exploitation material was found in his possession two months later on July 19.

He was charged on September 3 that year and then subsequently hit with further charges and arrested on October 3.

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He was dead 15 days later, before facing trial.

As opposition members continued to question Mr Shelton and Police Commissioner Darren Hine on the matter today, the pair remained tight-lipped.

"I won't discuss the individual case because there is now a commission of inquiry," Commissioner Hine said. "I'm not going to add to any further specifics about the case. We'll certainly cooperate with the commission of inquiry."

Franklin Greens MHA Rosalie Woodruff again asked Mr Shelton why he hadn't passed on the information to the relevant ministers.

"Now that we understand the scale of what happened, we look at your actions with that knowledge and we ask why other colleagues responsible for child safety, education and health weren't informed," she said.

"Of course, from an operational point of view, it was an ongoing investigation," Mr Shelton said. "Therefore, I don't get involved in ongoing investigations or, in fact, talk about ongoing investigations."

Dr Woodruff said this was a "shameful abrogation of your responsibility as a Minister of Police".

In a statement provided to The Examiner after the hearing, Mr Shelton said it was "completely irresponsible" for Labor to suggest he should "interfere or disclose matters that are subject to serious ongoing police investigation".

"These claims are staggering and only prove Labor are not fit for government nor do they understand basic protocols that must be followed to ensure there is no corruption of justice," he said.

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