Each state has different filing requirements. Check the filing requirements for the state that your college is in. With only two months' income, it's possible that you don't have to file, depending on the state's rules. But if state tax was withheld from your pay you might want to file to get a refund of the tax that was withheld, even if you are not required to file.
Each state also has its own definition of a resident, and the definition of a resident for income tax purposes might be different from the definition for other purposes. Usually being away at college does not make you a resident of that state if you lived in a dorm or other temporary housing. If you do file a state tax return, but you do not meet the definition of a resident, you would file a nonresident tax return, not a part-year resident tax return.
You might also be required to file a federal tax return and a state resident tax return for the state where your permanent home is. You can use the calculator at the following link on the IRS web site to see if you have to file a federal tax return. Again, if federal tax was withheld from your pay you are probably entitled to a refund of the tax that was withheld, so you might want to file even if you are not required to.
Do I Need to File a Tax Return? (federal)
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