WITH THE enormous growth of the fine arts auction business in Washington, not to say the hot and high-priced real estate market here, no one is at all surprised that Sotheby Parke Bernet is opening a Washington office.

At the same time, the local auction house of C. G. Sloan's is opening a branch office in Baltimore. The Sotheby's office has just opened at 2903 M St. NW, in Georgetown.

Joan Tobin, a Washington businesswoman, philanthropist and political figure is heading the new Sotheby's office. She said Sotheby's will not hold auctions in Washington at first but hopes in a year or so to have auctions in hotels. One big on-the-premises estate sale is already scheduled on the Eastern Shore.

The Washington office accepts consignments and arranges to pack and ship goods to Sotheby's auction centers, such as New York City. The office also offers appraisal services and advice to bidders, including selling them the colorful and highly prized catalogues of auctions.

The real estate division here is headed by Samuel F. Beach, formerly with National Savings and Trust. Sotheby Parke Bernet International Realty Corporation, has been busy in this area for some time. Edward Lee Cave, a native Virginian, is chairman of the corporation and Charles H. Seilheimer, of Warrenton, Va., is president of the real estate division. hCurrently, it's offering Pokety, the 480-acre Eastern Shore home of the late Bernice Chrysler and Edgar Williams Garbisch, for $3 million, and Brice House in Annapolis for $1.4 million.

The first big area sale after the new office opens will be the on-premises auction of American antique furniture and decorative art at Pokety May 22-24.

Art and antiques from Sotheby's spring auctions, including the Americana collection of Edgar Williams and Bernice Chrysler Garbisch will be shown May 5 at a Folger Shakespeare Library benefit "Heirloom Discovery Day" to celebrate the Sotheby's opening.

Best of all, from 10 to 4 p.m. May 5, you can have the chance to find out if the teapot you bought in that dusty junk store is really the rare Chinese Export treasure you hope it is. A $15 ticket (proceeds to the Folger) entitles you to a series of short lectures on the art market, furniture, Russian art and Art Deco during the day -- plus verbal appraisals on three of your own objects. Coins, books and textiles will not be appraised. The expert will only tell you what it may be worth. Verbal appraisals aren't valid for insurance or estate matters, but they can give you an idea of what you have. You can have more objects appraised for $5 each. If it's too bulky to bring to the Folger, a good clear picture may do.

From Sotheby's will be Hugh Hildesley, head of client-services; Robert Wooley, decorative arts; Gerald Hill, Russian works; Letitia Roberts, porcelain; Barbara Deisroth, 19th/20th century; William Stahl, American furniture; James Lally, Chinese objects; Alison Bradshaw, jewelry; Sam Blaisdell, appraisals and Helen Lally, fine arts. Tickets are on sale at the Folger. For information call 298-6722.

John Marion, president of Sotheby's, said it was helpfulness that got Joan Tobin the job running the Washington office. "She wasn't working for us at all, but she was so helpful at finding us an office space and thinking about what we should do in Washington. We said, ever so hesitantly, not expecting we'd be so lucky, 'Would you run it for us?' And to our great pleasure, she said she would. I think she's a dynamic businesswoman."

And he might have added that she is a real Washington business person with a knowledge of what makes it all go. As did everybody else, she came to Washington with a candidate: former Sen. Robert Taft, Jr. from her home state of Ohio. (She's from Cincinnati.) She came to Washington in 1971 to raise a quarter of a million dollars to pay off his campaign debts. Her first direct experience in politics had been as assistant to the head of advance and scheduling for Nelson Rockefeller's presidential campaign in 1968. "But that job didn't last long," she said.

Somewhere along the line, she switched over to the Democrats. And in 1976 she was national coordinator of Jimmy Carter's Committee of 51.3 Percent, the women's support group, named after the female percentage of the vote."To remind them of how much we counted," she said.

For Carter, she organized and developed the National Women's Talent Bank, to list women capable of holding important government jobs. "So they couldn't use that old saw," she said, "'We'd like to appoint a woman but we can't find one that's qualified'."

Her business background all centers around management and money. She's president of Tobin Enterprises, a venture capital company; vice president of Tobin International, an import/export company; an adviser on business management, chairman of the board of several small companies ranging from clothes to plastic bags; director of COMSAT, the Communications Satellite Corporation, and U.S. permanent representative to INTELSAT.

Her husband, an attorney who's been in Washington for 25 years, is president of the National Theater. Joan Tobin is on the board of the National Theater and Ford's Theater here, as well as others in New York. She's also on the board of the Corcoran and several other civic groups.

Sotheby, which, as Joan Tobin, the director of the local office here, has "just realized is a multi-national corporation," has long skimmed off some of Washington's auction business, both buying and selling. But in the last year or two the C. G. Sloan and Adam A. Weschler & Son, the Washington auction houses, have had a tremendous increase in their own business, both local and out of town. There's no doubt that the current sales figures of the local houses have done a great deal to entice Sotheby's down.

C. G. Sloan auction house had sales of $5 million last year, expecting $7 million this year. Last year, Adam A. Weschler & Son had sales of $3.5 million and they expect them to go to $4 million this year. Both William P. Weschler of Weschler's and Russell E. Burke of Sloan's said they think that Sotheby's will help the auction scene here, not hurt it. "A concentration of good people adds to the ambience of Washington as an art center," said Burke, Weschler said, "They'll get their share and we'll keep ours. Competition is good for us. Auctioners are a friendly group of people. As for appraisals, well, we have more than we can handle. We're booked up through June."

Sotheby's in North America, had net sales of $147,337,000 in its fiscal year ending in June 1979. (The world-wide total was $412 million.) This year looks better, with sales from September to December 1979 along amounting to $91.4 million. Last year's sales were $35 million more than the previous year's.

Both Tobin and Marion say they think the business is depression-proof. "So far," said Marion, "we've had no reason to worry. Consignments are up and so is the interest. And of course, Washington real estate is the top market in the country -- all those people selling and buying houses every four years."

Sotheby's most recent spectacular was the sale of Frederic E. Church's "Icebergs," for $2.5 million in New York. The company, which began in London in 1744, has salesrooms in New York, Los Angeles, Zurich, Amsterdam and Canada, with 37 offices over the world.