Tasmania's Public Health department remains responsible for enforcing its quarantine measures, with police not involved in coronavirus isolation checks.
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Despite reports of "random police checks" in other states, Tasmania Police said on Tuesday it had not yet been approached by the Director of Public Health.
A public health emergency was declared in the state on Tuesday morning, which will provide the Director of Public Health with emergency powers.
In a statement, the Health Department said the powers included "directives to require a person to quarantine or isolate, require a person to undergo a clinical assessment, ban entry of people to an area or remove people from an area, and take any action required to manage the threat coronavirus poses to public health".
"These emergency powers will initially be used to enable the banning of mass gatherings and the requiring of people arriving in Tasmania after overseas travel to enter 14 days of self-quarantine from the time of their arrival in Australia."
Acting Director of Public Health Dr Scott McKeown said on Sunday that Public Health Services staff would complete daily checks for those in quarantine, until their 14-day isolation period was complete.
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Police Association of Tasmania president Col Riley said while police would "always do what was needed to protect the community", resourcing was already under pressure.
"Police have a limited capacity in this state, and I'm not confident that it would be the best use of resources.
"Someone needs to police it, and whoever does it needs to be properly equipped so they don't become infected, and they don't transmit any potential infection to members of the public.
"Ultimately, police officers will always do whatever they are told to do, and whatever they need to do, to keep the community safe."
So far, there have been at least 361 cases of coronavirus nationally.
Five people have died.
In New South Wales, people and businesses are facing fines of up to $11,000 if they fail to comply with mass gathering bans.
While failing to self-isolate for 14 days after entering Australia could mean fines of up to $13,000 for Queenslanders and up to $20,000 for Victorians.
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