Simple answer: no. But, as the other replies indicate, it depends on the details. For most college students, who are still dependents of their parents, their home state is where there parents live. This is true even if you live off campus, at school.
But, if you earned income in the state where the school is, you may have to file a non-resident state tax return and pay income tax to that state, You still have to file a home state return, but your home state will give you a credit for what you pay the non-resident state. Some states have reciprocal agreements**, in which case you file only a home state return.
** List of reciprocal states: https://ttlc.intuit.com/community/state-taxes/help/which-states-have-reciprocal-agreements/00/25576
