Apologizing for the accident may indicate that you are at fault—something that might not be true. While you may feel sympathy toward the other driver, refrain from accepting blame or apologizing.
An insurance company may use your apology against you if you pursue compensation. It is best to remain quiet and not speak with the other driver immediately following a serious accident.
Do speak with responding law enforcement officers, however, at the accident scene or the hospital. An official police report can serve as valuable evidence for your possible case. If an officer cannot determine fault right away, your lawyer can investigate and maintain communication with law enforcement on your behalf.