Thank you so much for your in detail and thoughtful answer. So the question asking: Have you ever committed a crime or an offense for which you were not arrested? The answer would be "no" I guess because I was accused of but not committed a crime... Is that right? And also is this issue would be a crime or an offense or a disorderly conduct? I will very likely to disclose it during the interview because it bothers me. But when they do background check to verify the application form info, this issue would not be picked up because no police was involved, is that right? I really appreciate your help.
Correct, the answer would be "no" because the police were not involved. If the police were not called and charges were not filed, then you would mark "no" on the form. You can mention it during the interview, but be sure to bring documentation that you have no criminal record because the officer may ask for it.