Just an update to add to HalAl's answer. Virginia has a "statutory" tax resident based on the number of days you are in the state so you would have to file the Virginia tax return as a resident. In most cases this does not apply to students but in Virginia it does.
You will want to file the Virginia tax return first, then you will be able to claim the credit for the taxes paid to another state on your Ohio tax return so you will not get double taxed at the state level.
Students are subject to the same rules for residency and filing requirements as all other filers. For example, if you lived in Virginia for more than 183 days during the taxable year, you are classified as an actual resident, and must file Form 760 even if you maintained your legal residency in another state. If you maintained legal residency in Virginia, but attended school in another state, you are still considered a Virginia resident and must file Form 760. If you had income in the other state, you may be required to file in that state also.
Residency Status | Virginia Tax
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