Does there need to be physical contact for an assault charge?

I had a disagreement with a bar owner who put his hands on my girlfriend while asking us to leave. He visibly shoved her and I turned and gave him a nasty look and told him I'd see him around. Apparently he knew who I was and contacted the police. He also claimed that he felt his life was in danger. My feeling is that it's something people say when they are mad. It was more smack talk than anything else. I really didn't have any intention of stalking the guy and hurting him or anything, I just got mad and said "see you around".