How to apply for a faculty position elsewhere without revealing the conflict with current dept chair? I am a new faculty member. My chair is simply crazy in my perspective.

I am an assistant professor. However, my teaching assignment is "offering individual statistical consulting/workshops", not "teaching any classes". This was indicated in my job description when I applied for this job. However, several times, she says, "you are not teaching" - so she says that I need to do what she asks me to do because she pays my salary (I really do not know why she pays).

What she wants me to do is to write research/funding proposals and articles, then put her as the PI/the first author although they are my research ideas/works. She has taken three studies so far. More seriously, when she took the first one, I refused it. Then she sent out an official letter including some other faculty, saying that she took my research proposal because it was originally her idea and I stole it. Worse still, she then forced me to write the paper for her.

My Ph.D. is in statistics. She said that I couldn't get tenured unless I change my research field into an education field which she wanted to do. Her point was again "paycheck" - I should do something because I am not teaching.

Worst of all, she claims I am a bad person and faculty member because I refuse her unethical requests as a researcher. Furthermore, she talks about me to all the other faculty members, causing them to hesitate to be friends with me. Whatever I say goes to the chair.

Anyway, I am leaving - what should I do to be free from the chair in the application procedure. I really do not want anyone to contact the chair as my referee. By the way, I wouldn't mention my chair in anywhere on my application documents.
Good search committee members are aware that many applicants do not want their current department to know that they are applying for a job. Search committee members should only be contacting your listed references. That said there are plenty of bad search committee members and plenty of search committees that accidentally let information leak out.

It is perfectly reasonable to not list your current chair, or anyone from your current department, as a reference. You should, however, list your current position on your CV. Not listing your chair as a reference does not mean your chair will not get an informal phone call, but there is nothing you can do about that. You should also know that when a department chair gives a reference, they often highlight the good aspects, and ignore the bad aspects, of people they want to get rid of and focus on the bad aspects of people they want to keep.