No cases have been recorded since 31-year-old Timothy Andrew Gunn escaped the Hobart Travelodge early last week and spent about 18 hours in the community.

It sparked a three-day lockdown across the state's south, including Hobart, which was lifted at 6pm on Monday.

Mr Gunn has already been fined more than $1300 for breaching quarantine, with other fines possible.

He apologised during a Channel 7 interview on Tuesday, claiming he didn't escape but simply walked out.

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Tasmanian Premier Peter Gutwein said the circumstances of the breach were subject to a police investigation.

"I expect to have a report from the state controller in coming days and we'll release that information when it comes to hand," he said yesterday.

Donna Adams, acting deputy commissioner of Tasmania Police, said two scenarios would be examined, that the man left the hotel out a window or via a door.

"The veracity of the claims made by the positive case will be assessed by Tasmania Police," Ms Adams said. She said security guards at hotel quarantine facilities didn't necessarily have the power to physically detain someone who attempted to leave.

"The expectation would be that security call police. Police are well trained to deal with difficult and non-compliant people," Ms Adams said.

"The last thing we want is untrained security guards to be grappling with someone seeking to leave a facility."

Of the 169 contacts of the man, 167 have tested negative and two results are pending.