I was accused of harassment by a coworker in the state of New Jersey.
I asked the HR Director who was accusing me. She told me they did not have to tell me.
I know it is my right to know.
Is it written in a law or something stating that I have the right to know so I can defend myself?

I'am facing the same problem I had to quite because of what they said. My boss would not tell me who said it only that it was a patient and she would not tell me who the employee was that I was to have touched. I'am 51 and cant believe this has happened to me. :(

Under the EEOC's own guidelines, the alleged "victim" has the right to remain anonymous until an EEOC complaint is filed. Since your employer is handling this on behalf of the employee and there is a good chance it will never get to the EEOC level, you may not have the ability to learn the name at this point.

However, once disciplinary action occurs, you can file a lawsuit against your employer. At that point, an attorney may be able to subpoena that information. Of course, use of an attorney can be expensive.

The right to secrecy is very different than criminal law, where an accused has the right to information about his/her accuser. However, it is a legal practice under employment laws.