If the other party called the police after you drove off, then it will be a hit and run and basically you loose your drivers license normally for at least one year. ( IN Georgia) The fact you gave them your info, may be a defense to it, and you will need an attorney.

1. Was this the same car that you said drove off to start with ? If so, where did they go and come back
2. Or was it a different car ?

Most likely expect them to have or claim 1000's of dollars of damages, most likely some medical bills and they will threaten to sue you, and then settle with your insurance company. This is a fairly common scam, most likely he drove off at first to get other people to be witnesses. ( my guess) So report it all to your insurance company, if they contact you don't talk to them, just turn it over to insurance company