College students are considered to be temporarily absent from their home state. Therefore, you will probably have to file tax returns in two states—your home state and the state where you are doing your internship.
Your employer will probably withhold taxes only for the state where you work. Don’t worry. Your home state will give you a credit for tax paid to the other state. But you will have to file a return.
Some states have reciprocal agreements, meaning you only have to file a return for your home state.
Which states have reciprocal agreements?