Where is your domicile?
Your domicile is the location where you have a permanent home, the place where you will return to when your sojourn out of state has ended.
It is common for college students who are away at school to retain the domicile of their parents' home.
When you went to Ohio, did you change your driver's license to your location in Ohio? Did you register to vote in Ohio? Did you buy property to live in in Ohio? Did you inform the Post Office that your new address was Ohio? All of these factors go into the decision of determining where your domicile is.
In your case, it is possible - but it depends on your facts and circumstances - that you were domiciled in Wisconsin up through college and through the summer, and then when you moved back for grad school, you changed your domicile (i.e., you did not intend to return to live in your parents' home). In this case, you would file a part-year return in Wisconsin and a part-year return in Ohio. But if you always maintained your domicile (which is different than where you happen to be sleeping) in Wisconsin, you would file a resident return for Wisconsin (if required), and a nonresident return in Ohio if you had any income there (again, if required).
But as I said, it depends on your facts and circumstances. Please read the instructions for both states what a "resident" is, and then if you still have questions, come back and ask.
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Students are considered residents of their home state, not the state the school is in. You report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state. You will have to file a non resident OH state return and pay OH tax on the income earned there.. You will also file a WI full year resident return and calculate tax on ALL your income. WI will give you a credit, or partial credit, for the tax you pay OH. So, there will be little or no double taxation. Do the nonresident state return first.