Waterford Police say the group made reservations online but were turned away because they did not meet the residency criteria.
The average age of those in the group was about 80.
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According to police, no one was arrested.
Connecticut is currently ranked fourth in the country in distributing the vaccine.
And Governor Ned Lamont says the state will not bend its rules.
"You've got to live here in Connecticut or work here in Connecticut," he said. "You've got to identify yourself as such when you sign onto that CVS site to make that appointment for your vaccination. You're going to have to show proof of where you're from, and you're going to have to prove you're over the age of 75."
In addition to those meeting the age and residency requirements, people eligible for vaccines in Connecticut include healthcare workers and medical first responders who face a risk of COVID-19 exposure; and long-term care facility residents and staff members.
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