It depends on the circumstances. If an employee injures someone while carrying out his job, the company will almost certainly be liable to the injured person. For example, if a delivery driver for a florist hits a pedestrian while rushing around making deliveries on Valentine's Day, the pedestrian can sue the company for damages. At the other extreme, if an employee hurts someone while off-duty, with no connection to work, the company won't be liable. For example, if that delivery driver sings in a band on the weekends and injures a fan by knocking over a tower of amps, the company can't be sued.
Your company may also face liability if it hires or retains an employee whom it knew -- or should have known -- posed a danger to the public. For more information on when employers can be sued for injuries caused by employees, see Nolo's article Employer Liability for an Employee's Bad Acts.
For legal advice, you'll need to talk to a lawyer.