One of the things that I have always thought appropriate was to have your attorney's phone number on speed dial. If I am ever involved in a serious incident my order of priority responses will be:
1. Call my attorney.
2. Tell him what happened.
3. Let HIM call the police for me.
4. The first words to the police will be, "I will be more than happy to talk to you after my attorney has arrived here." Then remain silent.