single vehicle accident

I was driving home at 3:30am yesterday and lost control on some ice and collided with a curb and a sign post. I was near my home and was able to drive the car home (damage to the undercarriage and the right door). I have filed my police accident report (there is a few thousand dollars worth of damage because a side airbag deployed and the exhaust and connected parts were damaged by the curb). I was NOT drinking at the time or at all on Friday. My question is how does the claims process work with regards to this? Will they assume I was drunk solely because of the time of day(the police officer seemed to have this mentality and repeated questioned me about it)? if so how much will they investigate it? As I was coming back from a friend's house whom i do not know too well, and her friends even less, will I be asked to track them down?