MetLife will pay at least $50,000 in penalties and refund an undetermined amount of money to customers to settle allegations it imposed costly surcharges on Massachusetts drivers who were found not at fault in auto accidents.

State Attorney General Martha Coakley said Tuesday that some customers of Metropolitan Property & ­Casualty Insurance Co. — a unit of MetLife — who filed accident claims with the company were improperly ­penalized even after a state appeals board ruled they were not responsible for causing the crashes.