If I was in a car accident, can I pursue the person that actually hit my car's insurance or my only option is to find out that person's insurance?

I was in a car accident. While at an intersection, the light turned green as I barely started to proceed, I scanned to the left and noticed a car running a red light so I immediately stopped and attempted to avoid it by turning to the left. It was not a far distance at all since I barely began to accelerate then came to a full stop. However the car that was on the opposite direction, it was driving east in the intersection and I was driving west while the other car was driving north, was not so lucky and was t-boned by the other vehicle. The speed of that car caused the other vehicle to come right into me and all I could see was that a car was coming straight into me, with what seemed at lightening speeds. That car ended up on its side and up against my car, although it seemed as it was going to smash into the top of my car from the direction I was looking and all I could do was brace for impact. The car that ran the red light left his car at the scene and took off. My question is, since there is no information currently on the hit and run driver and the police report places him at the at-fault driver. Locate the owner of the vehicle? The easier choice would be the person that hit me since I have that person's insurance information. My vehicle only had liability coverage.