Now, when I lived in University Height OH, in the early-mid 90's my neighbors told me about this "perk".
There were many families of the town, which children went to private school, and not the local public elementary school.
My neighbor told me since there children went to private school, they could get a "tax break" on the local school tax, since the child did not go there.
Where as my child would have gone to the public school (he was only 2) the funding was horrible.. School Levys made the taxes go UP every year that we lived there.
This was a long time ago. Now if this "perk" is still there, I don't know.
My parents have a beef about this. The town in which they live has no police department (closed), no paid fire department (volunteers in their pickup/SUV's), some roads are still dirt/gravel, the library is only open two days a week, and the school is still using a 1920's building... and they still pay thousands of dollars for property tax. ( I want to say in the $3-4K range!)