The Ohio state website indicates that, beginning in tax year 2007, if you are an Ohio resident stationed outside of Ohio, you can exclude your military income from Ohio adjusted gross income. Therefore, no Ohio or school district tax will be calculated on the active duty pay.
If you are a nonresident of Ohio, your military pay is not taxable to Ohio or any School District. However, any income earned other than active duty military pay that is excluded on the return is subject to Ohio tax and the School District tax.