I have only known my district manager for a couple of months and worked with him for a week about a month ago. Since then, I only talk to him on the phone once a week to go over reports. He was in the office last week and we spent the afternoon together on a project.
He asked if I had a problem with him and I told him "no" and I wasn't sure what he was talking about. He told me I seemed distant and my body language was tense around him. He said he feels like there is tension between us and I said there wasn't. He then told me when he was in the office once, I looked at him and didn't say anything and he talked to his friend that night about that and I told him I was probably just busy because I didn't remember.
For three hours he kept going over and over it and how he feels tension with us and how my body language tells him I am distant. I asked him if I have ever been unprofessional or disrespectful to him and he said no so I don't know what he's talking about. I did tell him sometimes I think we have a communication barrier but it was no big deal. He focused in on that and we went through some role playing on how to communicate better which took like an hour. We don't work together directly and I've only spent time with him a week so I don't see what the big deal is.
This really caught me off guard so I'm not sure if he's got a personal problem with me or is just making this personal for another agenda he may have. I'm a little concerned because this was a very unusual conversation considering he doesn't really know me. He also told me he doesn't care what people think of him and just does his job which contradicts why he was so focused on what I think of him and why he spent all afternoon going over this. I don't understand where he's coming from or why he did that. A part of me thinks he wants my attention and another part of me thinks he may be trying to intimidate me. The next couple of days he completely ignored me and acted like that never happened so I guess he just wanted to catch me off guard or make me feel insecure?

Anybody that holds a position of authority over you, that makes you do things that make you feel uncomfortable, is a bully.

That, after several hours of not accepting your (reasonable) answers to the 'barrier' between you, and the role playing, is nothing more than a sick power play, meant to make you feel uncomfortable, and let you know he's boss, and also to let you know what he thinks he can and cannot do.

My gut says that he has been a problem to other people as well, but that is beside the point.

You are in control here. Only you. When he approaches you with this b.s. again, or something along those lines involving only him and you, politely excuse yourself, and ask him to first run this by his supervisor, because YOU don't think his behaviour is appropriate.

Short and simple. You must stand up for yourself, and in so doing (as it is with most bullies) he will back off. All he needs is a harassment claim through the company, and he knows it.

Because you are new, also like bullies do, he has you in his target range. Because this happened in the workplace, and he is your superior, accept that it makes you uncomfortable, and don't ever let yourself be in such a position again.

If the conversation had happened at a bar, about your body language etc. you would have thrown a drink in his face, and rightfully so.

He has no business acting in such an unprofessional manner.

I think this guy is weird and has an agenda unrelated to work. He's trying to make you feel there's something wrong with you so he can manipulate the authority he possesses as your boss. I would suspect he may wish to escalate this into a personal relationship.

I would suggest you do your best to avoid being alone with him.

The other option is that he's just plain paranoid and nuts.

If you don't see him often this may be manageable, but if he pushes this agenda with you, it's possible you will have to leave the organization. As stated above this kind of behavior is bullying and a warped effort at control.