Can we require workers to wear their company t-shirts only at work?

Q: “Our employees are required to wear company polo shirts with our logo on them while they are working. They paid for the shirts through a payroll deduction. Can we tell them they can only wear those shirts while on duty and not any other time? We fear that someone might wear the shirt on his or her own leisure time while doing something that misrepresents our company’s values.” – Bill, New York