What state and what School District?
The school district tax (in most states that have one) is an income tax and levied on the same income that you pay state income tax on. It's unrelated to dependents still in school.
Some SD income tax (SDIT) is an earned income tax, so it would only be paid by people still working (retirement and investment income is not taxed).
Age exemptions are rare (if any even exist)
