When I had my accident I submitted to Chase the online accident report which I filled out for the state, but I didn't include the form from the car rental company which I had also filled out. Of course, I also submitted the damage estimate letter once I received it. It took the car rental company about 5 weeks after the accident to send me that letter.

Unfortunately, an accident with a rental car necessitates keeping track of a lot of paperwork. But once you get the initial claim form filled out you're mostly just waiting to hear back from the various parties involved.