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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