No. Ohio allows an income deduction for the 529 contribution, not a tax credit. For example, if line 5** (Ohio income tax base) would be $50,000 without the 529 contribution, it would be $48,000 with a contribution and line 8c (your tax liability) would only be about $70 less.
Nor is the contribution treated as a tax payment. That is, it does not go on line 18. The $2000 is entered on line 31 of Schedule A and transfers to line 2b (along with any other deductions on Schedule A) of form IT1040.
Ohio now allows up to $4000 for 529 plan deductions per year. Any excess carries over to next year. A $4000 deduction is worth between $80 and $200, in state tax savings, depending on your tax bracket. That assumes that line 10 was not already 0, without the deduction.
** For most people, lines 7 (and 7a), of form IT 1040, is the same as line 5
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