Sotheby's, the world's largest fine art auction house, announced today that it will close its salesrooms in Los Angeles and on Madison Avenue in New York in September. The company said it will consolidate its U.S. operations at its only remaining U.S. salesroom, at York Avenue and 72nd Street here.

An official said the firm also was considering closing the company's Toronto salesroom.

Four months ago, the firm closed its salesroom in London's Belgravia district and trimmed its activities and staff in other British cities. At the time, it blamed its financial problems on the recession.

The Madison Avenue salesroom, located at 76th Street in the center of New York's art marketplace, is the site of jewelry and fine art sales and houses the North American corporate offices of the London-based firm. The Los Angeles salesroom, with annual sales in the neighborhood of $20 million, is located on Beverly Boulevard in Hollywood, next to CBS' studios.

The other Manhattan salesroom, on York Avenue, was opened in September 1980, to house sales of decorative arts and to ease overcrowded conditions on Madison Avenue. It is twice as large, but several long blocks from the established art market center. Joseph Hirshhorn's furniture and Winston Guest's silver have been sold there.

Sotheby's leases its space at both the Madison and York Avenue salesrooms. It reportedly has long leases at both locations.

Immediately after today's sale, in which the Rosebud sled used in "Citizen Kane" was sold, the entire staff of both salesrooms was called to an emergency meeting that lasted about 40 minutes. Also attending were Graham Llewellyn, president of Sotheby's, and Gordon Brunton, its new chief executive.

According to John Marion, president of Sotheby Parke Bernet Inc., the firm's New York branch, "We have realized that it is far more effective and efficient to sell all property under one roof. In addition, there will be substantial cost savings, which plays an important role in our worldwide cost-reduction program."

Cost reductions are apparently necessary at Sotheby's now. Pinched by the recession, the firm refused for the first time to release its first-season net sales turnover, sparking a vigorous debate about the health of the company. In 1980-81, the firm posted net sales turnover of $300 million in North America. Although 1981-82 figures will not be out until July, several well-informed observers suggest that sales might have dropped to $200 million for this period.