Anyone with coronavirus symptoms in Devonport will be able to be tested, Public Health says.
Deputy director Dr Scott McKeown said Public Health was continuing to trace the contacts of two people confirmed with the virus at Devonport.
"We are nearing the completion of those investigations in the community and there's also an ongoing investigation within the Tasmanian Health Service," Dr McKeown said at Friday's coronavirus media briefing.
"We're also implementing a process of testing in the community called sentinel testing, in which five general practices and the Mersey Community Hospital will undertake testing of anyone presenting with suggestive symptoms.
"To get a sufficient number of tests that will take into next week before we're able to provide publicly any information on our finding.
"If we do find confirming evidence of community transmission we'll respond earlier."
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Like Pemier Peter Gutwein, Dr McKeown was heartened that the rate of COVID-19 cases is dropping but warned that strong measures needed to stay in place to prevent the spread of the virus.
The number of cases daily has dropped to around seven per cent nationally and by five per cent in Tasmania.
Dr McKeown said the slowing of cases was encouraging.
"Towards the end of last week and the weekend, we had a significant spike," he said.
"We're seeing now slowing of those cases and that's very reassuring for the Tasmanian community.
"Much of the driver of that are outrvery strong measures that we're putting in place. But I need to stress to the Tasmanian community, now is not the time to be complacent.
"COVID-19 is a very serious disease.
"The measures that we are recommending and putting in place and requiring are very important to be continued so that will ensure that Tasmanians protect themselves and other members of our community."