Most public school systems in the United States do not. Counties/school systems with a large Jewish population often do; it’s usually predicated on estimates of what percentage of students (and faculty/staff) will not attend school on Jewish holidays anyways. If that percentage is significant enough, school is out for everyone.
Did/does your local public school system close for Jewish holidays?
If you don’t know, here’s a handy map where you can check if your county does (they’re colored in blue).
When I was in school we were definitely always off for Rosh Hashanah and Yom Kippur, I don’t think there were usually others but I could be wrong.