The D.C. Public Service Commission approved yesterday the request of the Washington Gas Light Co. to hook up 3,000 customers.

The decision means that for the first time since 1972 new natural gas service will be available anywhere in the District. Since the moratorium on new customers was imposed because of gas shortages, new connections have been permitted only in the 1968 riot corridors.

Washington Gas earlier received permission to serve 3,300 new customers in Virginia and 4,300 in Maryland; it already has begun making connections in Virginia.

The resumption of new natural gas connections will probably mean lower heating bills for homeowners who otherwise would have to heat with more expensive oil or electricity.

It also will help hold down the rise in heating gas bills for other customers, by giving the gas company a broader base of customers to share its fixed costs. The gas company said it had lost 7,000 customers during the moratorium and gas use had declined further because of energy conservation.

Following its practice with suburban customers, WGL will serve those who are on its waiting list in Washington first.

Washington Gas officials estimate they will be able to begin taking on new customers by mid-summer but could take as long as two years to use up the 3,000 additional openings.

The District's decision limits new gas service to customers using no more than 500 therms of gas on the average day during the peak month of use. Within that limit are all single family homes, most small businesses - including major gas users like car washes and laundries - and apartments of up to 75 or 100 units, said a PSC official.

The commission said it would consider exceeding that limit in special situations, such as for large housing-projects for the elderly or poor.

The decision also said customers now receiving interruptible gas service - which is cut off when demand is high - cannot cover to firm service under the new provisions.

Potomac Electric Power Co. opposed the new gas hookups, but did not mount a major case against it, PSC sources said.

In seeking to connect the 10,000 new customer in the three jurisdictions it serves, Washington Gas said natural gas supplies had improved enough to end the moratorium.

The gas company earlier this year began getting shipments of liquified natural gas imported from Algeria. Deregulation of natural gas also is expected to make some gas available in this area that up till now has gone to the intra-state gas market, where prices are not regulated.