Do you have to give a statement to the others insurance company if no police were called?

AnswerImportant: Always default to your own insurance company for this answer.

If the other insurance company is trying to contact you, call your claim representative and ask her what you should do. Usually, your insurance company can discuss liability with the other party's insurance company without you having to get involved. You don't want to prematurely call the other insurance company and say something on tape that may cost you a better legal standing.