Are Graduate Fellowships or Research assistants in state university considered a government employees in US?
It likely depends on the source of the funds. If you were paid by the department at a State university, then the likelihood is that it is a Yes. But if you were paid through a grant then the answer might be no, but might depend on some things.
I suspect you should ask the department, or, alternatively, answer Yes, but qualify it somehow/somewhere with the actual arrangement.
But, as Paul Garrett notes in a comment, things vary by state.