REalize that no citation does not mean no fault
It may vary by the state you live, but a lot of times it is easier to have your insurance cover the damages and then if they determine the other person is at fault they will subrogate the claim and try and get the money fro the other insurance company. If they win then they should get you any deductable that you have paid as well.
Your insurance company has more experience with this process than you so that is why I recommend letting them go through the process.