For state taxes, if I do not owe any amount or have no refund, do I still need to mail in forms?

[DanielV01]

It depends.  The first question is if you have a filing requirement in that state or not.  Not all states have the same standard for filing requirements.  If you comment the state, your approximate overall income, your filing status, and the income in that state, I can give you a specific answer on whether or not you have a filing requirement in that state.  Having $0 due is not a guarantee that you are not required to file.

The second question is whether or not you are e-filing.  If you e-file, there are probably no documents you need to mail in unless the state in question later asks you for them. 

Which means that you would have to mail in the forms if you have a filing requirement, and you choose not to e-file, but rather, mail in the state return.