I just posted this answer on Avvo. In short, the question is what do you do about a rental car when the insurance company for the at-fault driver is claiming they can’t get hold of their driver.
On the police report, go to buy crash.com and see if you can print one up. If you can, fax it to the insurance company. You want to take away every excuse they throw at you. They do have a reasonable amount of time to investigate the claim. If this guy proves to be uninsured, remember that you can make an uninsured motorist claim against your own policy. Moreover, I understand that uninsured motorist coverage can cover your property damage, depending upon how the policy is written, in Indiana.
If you pay for your own rental, keep your receipt and try to keep the cost low. There is no guarantee that they will reimburse you in full. FYI, usually a liability carrier will only cover a rental car for 10 to 14 days so you want to start looking for a new car. Also, they owe you fair market value for the vehicle, not the payoff. So get together your receipts and your title as you want to show it is worth as much as possible.
Lastly, if you have any pain at all, get to the doctor. You want to get to the doctor. Injury cases live and die on the contents of the medical records. As a result, if you don’t have treatment for a time period, it looks like you were not hurting.