I had gambling winnings from Indiana and I live in Ohio. Do I have to file state taxes with Indiana since The casino took out the state tax?

Casinos only withhold taxes. You still have an obligation to file an Indiana non-resident tax return. The withholding will be a credit against your tax, and you will either have a refund or owe a small additional amount of tax.

Your winnings must also be included in your Ohio taxable income.

The official answer is yes. You have IN source income and are required to file.

That said, they probably will not "come after you", if you don't, because they already got their money.

But, they probably took too much and there's a chance you have a refund coming.

Ohio will give you a credit, or more realistically only a partial credit, for what you paid IN.