I overheard my Human Resources Director make negative remarks about me and my character to another employee, while that employee was in her office saying that I did not do something. Is this ethical or even professional, and should I let the HR Director t

A coworker came into my office and was rude, and disrespectful towards me when asking a question and demanding an answer. She would not let me answer, she continually over talked me when I tried to answer her. She then wen to our HR Director and was complaining that I was unprofessional because all I did was shake my head and would not answer her. I overheard the HR Director tell the other employee negative things about my personality. Is this ethical or professional, and should I let the HR Director know that I heard her and that I feel it was not professional?