The US Supreme Court has ruled that the National Labor Relations Act gives workers the right to request union representation during investigatory interviews by supervisors, security personal, and other managerial staff.  These are called Weingarten Rights.
 
An investigatory interview occurs if 1) management questions you to obtain information; and 2) you have reasonable apprehension that your answers could be used as a basis for discipline or other adverse action.
 
You must ask for union representation either before or during an investigatory interview.  Management does not have to remind you of this right.  If your request is refused and Management continues asking questions, you may refuse to answer.  Your employer is guilty of an unfair labor practice and charges may be filed.  If you are questioned in a situation where Weingarten may apply, read or present this statement:

"If this discussion could in any way lead to my being disciplined or terminated, or affect my personal working conditions, I respectfully request that my union representative, officer, or steward be present at this meeting. Until my representative arrives, I choose not to participate in this discussion."