Do they do a nationwide background check when they arrest someone on domestic violence?

Normally yes. Although, if you are dealing with a very small town police department, it just depends on who you are. Example- let's say you went to high school with the arresting officer or you're in the vol. fire dept. with the arresting officer or his friends, cousin, uncle, brother or father-in-law. Chances are they will not do a nationwide background check if you are buddies with the law. It's not right but it's the world we live in and this answer is from experience!