How do I dispute a police report and prove that I was not at fault for a car accident?

Question Details: This accident happened on a two lane street. The mailman was on the right hand side of the road sitting at a mailbox with the flashers on. A vehicle in front of me signaled then got in the left lane and went around. The mailman was still just sitting at the mailbox with flashers on so I signaled to pass and got in the left lane to pass. As I was in the left lane passing, the mailman pulled off from the mailbox and swerved into the left lane and swiped the front end of my car my fender, passenger tire and a dent above the tire was hit by the front end/ grill of the truck. We pulled off the road about a half block from where i was hit and parked in a private driveway as it was safest out of the street. The trooper came about an hour later and got our statements. Few days later the police report states that I tried passing the mailman while he was making a left turn in a private driveway. This is not true and as a result places me at fault when I know 100% the mailman hit my car. The mailman lied and made it look like I hit him while he was already turning left. This is untrue. There is no way he was turning left at the private drive when that is where we drove to park after my car was already hit and secondly, if I would have tried passing while he was already turning as he stated I would have hit the side of his truck. I was in shock the trooper believed this when he clearly looked at how my car was all dented up and the front grill of the truck was hanging off. I even have the black scuff marks on my car tire rims and fender because my car is white and his truck is white with a black grill. I got hurt and went to the ER for neck pain and am currently under the doctor's care. The mailman's insurance company has written to me suggesting I repay them for the damages but I absolutely refuse because I know I was not at fault the mailman flat out lied and so far has gotten away with it as his vehicle is fixed. I know a lawyer will be the best option since I'm injured and don't have insurance but what can be done to prove my innocence if I got a lawyer? The insurance company already paid for his damage due to lie in the police report. I have been wronged and I intend to fight this no matter how long it takes.

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