Car accident! Urgent, pls help

My wife had an accident this afternoon at an intersection. She was driving with a green light, and was hit by another car. The other driver apparently had a red light.

Unfortunately, my wife forget to find a witness since she never ran into an accident before. When the police offer came, both sides said that they had a green light. My wife told the truth, the other driver lied.

Later, my wife saw an man who witnessed the accident, and was willing to testify before the police officer. He testified to the police officer that he heard the crack, and turned around and saw the green light in my wife's direction.

Would that be enough for the police officer and insurance companies to decide who is responsible for the accident? Anyone has good ideas?

Thanks for your help.