Four auto insurers have agreed to settle allegations that they failed to refund at-fault surcharges to Massachusetts customers, resulting in higher premiums — after a customer has been in a crash, for example — when a state appeals process sided with the customer, Attorney General Martha Coakley's office said Thursday.

In cases of a Massachusetts resident crashing a car, or another event that results in a surcharge causing a higher insurance premium, customers may appeal the insurer's determination of fault to the state's Board of Appeal. If the customer wins the appeal, the insurer is required to refund the surcharge.

Since 2003, the Board of Appeal has overturned more than 40,000 surcharges imposed by insurers.

The four insurers agreed to an audit to determine refund amounts. The insurers have made the following payments to Massachusetts, and will pay more depending on the results of the audit:

- Premier Insurance Co. of Massachusetts, a division of The Travelers Cos., $50,000

- Pilgrim Insurance Co. and Plymouth Rock Assurance Corp., a combined $50,000

- Massachusetts Homeland Insurance Co., $20,000.

Travelers spokesman Gary Griffin said: "We are working closely with the state of Massachusetts to resolve this issue and will refund affected customers. A fix has been implemented so on a going forward basis, current customers who have at fault accidents overturned are rated appropriately."

Coakley's office investigated insurers after a customer with Metropolitan Property & Casualty Insurance Co. — a division of MetLife — had a surcharge overturned in 2010 but did not get a refund from the insurer. MetLife agreed in January to pay $50,000.

"Our investigation has revealed troubling defects in the policy processing systems used by auto insurance companies," Coakley said. "While we are pleased to have secured the return of these overcharges for Massachusetts consumers, these cases underscore the need for insurance transparency and oversight."

Consumers who have successfully appealed a surcharge and but have not received a refund may call the attorney general's Insurance & Financial Services Division at 1-888-830-6277.