Determining state residency for a college student attending school out of state

It depends.  Tax law generally states that you are on a temporary absence when you are attending school.  Under this definition, you are technically still a Minnesota resident, which would require two returns:  an Illinois nonresident return and a Minnesota resident return.  The taxes you pay on your income in Illinois is counted as a credit on your Minnesota return.

This is not a clear-cut situation, however, for two reasons.  One, you did not return to Minnesota over the summer (which is "expected" for most who are away temporarily for school), and second, you state that you have no intention of returning to Minnesota.  While technically speaking you still seem to fit the definition of a Minnesota resident, you can at least reasonably argue that you no longer are, especially if you cannot be claimed as a dependent on someone else's tax return (such as your parents).  Under this position, file as an lllinois resident only.  Keep in mind, however, that Minnesota could argue that your income is taxable there and request/require a return, so you may want to have documentation handy to support your position.