If you have an auto accident on company time, whether your employer is "responsible" depends on what arrangements have been made in advance and what you mean by "responsible."
- Were you driving a company vehicle?
- Were you engaged in company business or on an errand for your own benefit?
- Were you complying with company policy regarding distracted driving, hands-free cell phone use, etc?
- If you were driving your own vehicle on company business, was that a routine process and had you notified your insurance company of that practice?