Can they come to the state where I am from and arrest me even if I'm not in the state’s custody?

It all started in a parking lot. The cops were coming at me head on and cut me off. So I stopped, put it in reverse and turned around, pulled out of the parking lot, hit the gas and drove about 2 miles then turned onto the on ramp and got on the express way and flew home. I didn't see any cops behind me at any point except at the start which makes me think they either didn't chase after me or they thought I went straight and didn’t get on the express way. They wanted to pull me over for speeding. I didn't want to stop for certain reasons when he cut me off in an unmarked SUV. I put it in reverse and looked behind me. There was a man not a cop. He was dressed in regular clothes, standing behind me and starting screaming don't run and cursed me. He punched my side window and I drove off. When I started driving, he either threw something hard or punched my back window. I heard a loud thump. If I ever get arrested and have to face the judge, my argument is going to be that I didn't know it was a cop. He turned his lights on but I'm going to say that I was turned around and didn't see them and that I thought he was a guy who was trying to fight me from an incident earlier on in the day and when I was turned around looking behind me to reverse and get out of there I saw another guy who I thought was his friend saying get out of the car and cursed me trying to fight and jump me. I got scared and drove off. I didn't see any lights and nobody chased me. I had no idea it was the police. Don't you think they would have followed me and turned their lights and sirens on if it was the cops that's why I had no idea. If I thought it was cops, I would have stopped. I live in another state about 90 min away from where it happened. Can they call the police and have the state pick me up?