Owners of General Motors cars who get into disputes with Washington-area dealers can take their complaints to an independent arbitrator, under a new program announced yesterday by the nation's biggest automaker.

When drivers and dealers can't agree on who should pay for repairs, a volunteer mediator nominated by the Better Business Bureau will make the decision, said James G. Vorhes, vice president in charge of GM's Consumer Relations and Service. GM also will pick up the tab for the service.

The Washington region is the 14th area in which General Motors has set up the program. It was started in Minneapolis in 1978 and is gradually being extended to the rest of the United States.

Ford Motor Co. has had a similar program for the District of Columbia, Maryland and Virginia since May 1979. Chrysler Corp. also has experimented with such a plan, but not in this area.

All three companies said the independent panels are meant to handle only complaints that can't be settled by the dealer, the regional office or the customer service department in Detroit.

The General Motors program covers dealers in the District of Columbia, Prince George's and Montgomery counties in Maryland; Loudoun, Arlington, Prince William and Fairfax counties in Virginia, and the city of Alexandria.

Washington-area customers who've exhausted the other remedies can call the Better Business Bureau of Metropolitan Washington at 393-8020. BBB President Douglas Tindal said his business-backed agency will first try to mediate the dispute.

If that doesn't work, the bureau will nominate a panel of volunteer arbitrators. One of them will be chosen by mutual agreement to decide the issue. After a hearing at which both sides present their cases, the arbitrator will issue a decision.

Vorhes said GM will use the system to settle all disputes over new car warranties as well as claims involving alleged manufacturing defects that show up after the warranty period. GM will not get involved in disputes between dealers and customers over sale of cars.

Under GM's plan, the arbitrator can't award punitive damages or order any payments beyond the actual value of repairs.

Vorhes said that as of last November, 2,500 complaints have been taken to the Better Business Bureau panels and about 2,200 have been settled. About 1,600 were settled by BBB mediation and only 520 required a full hearing.

In those cases, the arbitrator upheld the customer about one-third of the time and "generally substantiated" the company's position in the rest, he added.

GM officials said relatively few cases require a full-blown hearing. The possibility of an independent decision-maker intervening encourages both sides to settle the matter, they said.