Officials Warn That Vaccine May Not Be Available To General Public For Months 2 Photos Amagansett Fire Department member Britton Bistrian receiving the first dose of the COVID-19 vaccine at Southampton Hospital on Monday. A new COVID testing center will be open daily at East Hampton Town Hall from 7 a.m. to 4 p.m. Amagansett Fire Department member Britton Bistrian receiving the first dose of the COVID-19 vaccine at Southampton Hospital on Monday. A new COVID testing center will be open daily at East Hampton Town Hall from 7 a.m. to 4 p.m. Michael Wright on Jan 5, 2021 New York State is administering the COVID-19 vaccine to a gradually widening segment of the population and making preparations for distributing it to the general population — including launching a public web portal this week that allows residents to sign up for notifications about when they will be eligible to be vaccinated — but distribution is still limited only to healthcare workers or EMS personnel and is unlikely to be available to the broader public for several months.