Williamson County considering closing mass vaccination sites in May COVID-19 vaccine demand starting to level in Williamson County As the demand for the vaccines decreases they're thinking about the next step which includes closing these mass vaccination sites and letting The vaccine be administered through clinics and pharmacies. ROUND ROCK, Texas - The number of new COVID cases in Williamson County is dropping significantly. Officials in Williamson County attribute their mass vaccination clinics to the decline and say nearly half their population has received at least one dose. "We vaccinated around 375,000 people as of today. In fact, our supplies so far caught up with our demand," said Williamson County Judge Bill Gravell.