The state's Police Association is calling for priority COVID-19 testing of police officers after 11 staff were forced into quarantine this week.
Police Association of Tasmania president Colin Riley said police officers were critical in the frontline response, prevention and containment of COVID-19.
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"If government wants a task done they come to police. Whether it's checking on people in quarantine, stopping people getting off cruise ships or dealing with people in public places that are behaving badly and potentially have COVID-19," Mr Riley said.
Mr Riley said to have 11 staff forced into quarantine was significant, with five officers self-isolating as the result of an incident which occurred on Thursday night.
"We had a driver who was pulled over for an oral fluid test. He then took off and tried to escape and had to be arrested. Five officers had to get their hands on him," Mr Riley said.
"When we took him to the hospital to get blood taken to see if there was drugs in his system, he presented with having signs of COVID-19 and he indicated he thought he had COVID-19.
"What that means is he has to be tested and we had to put five officers into quarantine."
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Mr Riley said police officers should be tested and cleared as early as possible to get them back on the street.
"We can't afford to have them sitting for 14 days," he said.
"Police could be the vehicle for spreading [COVID-19] unless we are very careful about our quarantining, personal protective equipment and testing.
"We mustn't forget that our police officers look after elderly people and children with immunity [issues]."
Mr Riley said police had adequate personal protective equipment such as masks and gloves for now.
"But this is going to be a long haul and we need enough to last this incident out," he said.
Health Minister Sarah Courtney said all testing being done in Tasmania was in line with clinical guidelines and advice.
"If that advice comes that it's appropriate for certain cohorts in our community [to be tested] then we will act swiftly on that," Ms Courtney said.