I lived in one state but did not make money in it, as I was a student. Do I still need to file a state tax return showing $0 income and $0 taxes paid/

As long as you did not take steps to become a resident of the state where you attended school but had no income, you have no requirement to file a state return there.

Steps to establish residency in a new state include:

• Obtaining a driver's license
• Registering to vote
• Having important documents transferred to your new state (insurance, memberships, etc.)
• Establishing a local bank account 
• Filing a change of address form with the U.S. Postal Service
• Having a permanent home 

This list is not all-inclusive.  Also, please note that taking one or two of these actions does not automatically establish residency, and each state has their own set of requirements.