I imagine that this is going to be quite a mess to sort out....
First, regarding whether or not United offloaded the passenger within the remit of their Ts and Cs. Second if the Responsibility for the police being called will fall at the customer services/ complaint handling of United or Republic (who operated the flight) and thirdly, and most difficult if the physical injuries, and moral damage was caused by United or the Police service, I think that there is going to be a hell of a lot of finger pointing and posturing before any setlement is made. I also wonder if United/Republic/both will take the Police service to court for damages over this incident, as ultimately, the responsibility for the passengers injuries must lay at the feet of the officers on the aircraft.
I have no idea about my next question, as this resulted in the injury of a passenger onboard a US reg aircraft, will the NTSB get involved and make a report on the incident? or do they only care when the engines are running?