The state was recently placed in a lockdown after Albury man Timothy Andrew Gunn allegedly fled for about 18 hours after entering the state without permission.

Another person allegedly helped him leave the Hobart hotel.

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Mr Gunn, 31, was said to have been non-compliant with restrictions, including mask wearing, and uncooperative with authorities after being caught.

The southern part of the state was locked down after the incident, which was lifted yesterday.

Tasmania Police yesterday told The Border Mail the matter was still being investigated.

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

Premier Peter Gutwein yesterday said the state had been fortunate to avoid any further spread, which could change as his close contacts were tested.

Mr Gunn may be sent back to NSW after he is released from quarantine.

"That's obviously a matter for police," the premier said.

"They'll work through those matters."

At an earlier press conference, Mr Gutwein said authorities had struggled to trace his movements.

"Unfortunately the COVID positive man who absconded from hotel quarantine has not been co-operative, leading into inconsistencies and non-disclosure of information," he said on Friday.

Tasmanians have taken to social media to vent their frustrations in recent days.

The southern state has largely been COVID-free all year with only three cases.

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