As mentioned in other posts, I am in local government here in CT. Our area schools are closed first day RH and YK. Teachers may use personal days for religious observance, NOT sick days. Sick days are for illness. If a known Jewish teacher attempts to use sick days for Yuntif observance they will be asked to provide a doctor’s note for the absence.
Unpaid time will be granted for religious observance. After all, the municipalities have to pay substitute teachers to cover classes when a teacher is out.