Someone hit my car, no insurance, do i file a police report?

someone hit my car today. he was driving on a suspended license and had no insurance. it was 100% his fault and there are skidmarks to prove that he skidded into my lane (i was going the opposite direction than him) and i also have a few witnesses. i didn't call the police because he said he would pay for the damages (and he's worried about getting arrested). i don't care about the dents, but a friend looked at my car and said it looks like he dented my axle and messed up my suspension. i'm going to get an estimate of how much it will cost to fix and if its not thousands of dollars i'm going to trust he will pay me considering he can get in a lot of trouble if he doesn't and i tell on him. is it a bad idea to not file a police report? or should i just file an insurance claim and have them (i'm insured with state farm) pay for the damages and have him reimburse them? i'm just trying to not get screwed over and have him not pay me. what should i do