If you are a college student who is being claimed as a dependent of your parents, you are considered to have a "temporary absence" from the state your parents live in--so you are a resident of their state. However, if you worked in a different state then ---depending on the state--- you may need to file a non-resident state return for the summer job. You do not mention the states---which is important, since some states have reciprocal agreements with each other and some states do not have a state income tax. Provide some details.
I have a similar question that may serve as an example. We are residents of South Dakota, and SD has no state income tax. My daughter worked for the summer in Minnesota, attends college in Wisconsin, and has also worked there at her school. Does my daughter have to pay MN and WI state income taxes? We are claiming her as a depentant on our taxes, but she also has to file so we're helping her with her taxes.
Q. Does my daughter have to pay MN and WI state income taxes?
A. Yes, if she meets the filing requirements for each state. She will file a non resident return for each state.
For quick links to State Filing Requirements: https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/need-file-state-return/L446RvJAy_US_en_US?uid=m12jzvqq