Yes. Anytime you, as an Ohio resident, buy something at retail, you are required to pay use (sales) tax. When the vendor fails to collect it; you are responsible for remitting it to the state. To simplify the process, you may wait until after the year ends and include the sales tax on all your untaxed purchases as part of your income tax return (line 12 of form IT 1040). This question is part of the TurboTax interview.
This is not just an Ohio thing. Almost every state has a similar procedure.
