When you decide to permit an employee to drive a company vehicle or even their own vehicle while on the clock, you're opening yourself up to liability for any damage or accidents the employee may cause.t's also the job of a car owner to exercise due care when a third party is entrusted with the vehicle. If you failed to look into an employee's driving record, or knew or had reason to know that he should not be driving, then you may be held liable if he crashes a company car.