Weston First Selectman Chris Spaulding said there has been no gap in coverage with other officers filling shifts.
In addition to the police officers, one person in the department's communications center tested positive for COVID-19 as well.
After the first signs of symptoms, potentially exposed staff have been tested, Spaulding said.
"Weston is an incredibly resilient town with amazing staff and citizenry," Spaulding said. "The town is holding up well, given everything and with the continued help and resolve of our citizens, we will power through this challenging period."
As of Thursday, April 16, Weston had 42 reported cases of COVID-19 and two residents have died.
Town officials continue to encourage residents to stay home, following social distancing rules and wear masks when outside.
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