Car Accident Question?

I was involved in an accident. The guy was in front of the light and signaled left and when I went around him (I was a couple feet away) he turned right and hit my rear (which in my city is usually his fault for that. I asked him why did he signal left he said he did not signal at all. I told him if he did not signal at all then why did he turn right and we argued and later on went to the police station. Uhh we are both on liablity on our insurances. I was wondering do I have to call his insurance or calling my insurance and letting them deal with it is fine?