Let me suggest a quick flowchart for this question.
(1) Were you employed by a public University?
It's a bit hard to provide a comprehensive list of indicators for this. I've had both an employee and non-employee appointment as a graduate student at the same state University, so all I can say is that in my experience you should have received several clear indicators about the context of your position. "Research assistant" is usually a title of employment in the US in my experience.
- Did you sign appointment forms or letters when starting your position? If so, did those indicate you were an employee? Did they indicate that the position entailed specific responsibilities or who your supervisor was?
- Did your paystubs indicate you were an employee?
- Did the University withhold Federal income tax from your paychecks? If so you were probably an employee.
- Did you receive a US Federal tax form from the University at the end of the tax year indicating you received "wages"?
(2) Assume you were employed by a University run by a State. What you should do depends on who is asking about your status.
a. If you are applying to a job that is not in the same State as where you were a Research Assistant at a public University, simply say "yes". There is virtually no situation where an out-of-state asker cares about fine distinctions.
b. If you are applying to a job that is in the same State as where you were a Research Assistant at a public University, you should investigate this State's definitions more carefully via web searches tailored to exactly that State. This is the only situation I can imagine where the asker may care about pedantic distinctions.