A state supreme court decision in Arkansas underscores a fact that injured workers in many states come to find out: Injury lawsuits against co-workers are generally barred unless there is some evidence the action was intentional or outside the scope of employment.
That means the primary question is whether the incident was work-related. For example, if a co-worker physically attacks you, he was almost certainly not acting within the scope of employment, and therefore the victim would have grounds to file a third-party injury lawsuit, in addition to seeking workers' compensation benefits. However, if he negligently crashes a motor vehicle while the two of you are on your way to a mid-day conference, this would likely be considered an action within the scope of employment. That means workers' compensation would probably be your sole remedy for compensation from your employer, though it's always best to consult first with an attorney to explore all options as a lawsuit against the other driver or even against your own insurance company may be warranted.
In the case of Curtis v. Lemna, the high court found a corporate executive who crashed a golf cart during a game played as part of a sales meeting was immune from liability for injuries to a fellow executive because he was acting within the scope of his employment.