Insurance companies generally recommend not talking to the other party's insurance company. Your company will contact them. By talking to the other company you risk saying something that may be used against you.

You should call yourself. your insurance can only act on your behalf if they pay something out on your behalf (subrogation) so unless you want to use your collision insurance and pay your deductable youre best going straight through the other insurance. Also you should know that what the police said doesnt matter unless the police officer was standing on the corner watching the accident. Officers can issue tickets, they cant decide civil liability.