If an employee causes a customer an injury at the company, who would be held liable, the employer or employee?
The employer can be held liable depending on how the injury or harm was caused to the customer. Generally, if the employee was going about usual business, which may impose a risk towards customers or coworkers nearby (such as using a machine similar to one stores like Costco use to load heavy inventory on high shelves), then the employer would be held liable.
However, if the employee stepped out of his designated job duties and intentionally injured someone, then the liability may be completely be held by the employee. Personal injury torts and statutes vary by state to state to determine liability in cases such as this.