Dart Drug Corp. announced yesterday that it is planning to sell stock to the public in its fast-growing Crown Books subsidiary.

Robert M. Haft, president of Dart and of Crown, said that "preliminary discussions have been conducted" about the offering.

Though no details were announced, market analysts expect Dart to follow the pattern it set April 26 when it spun off its highly profitable Trak Auto subsidiary. Dart retained ownership of 68 percent of Trak's stock, and those shares are regarded as one of Dart's principal assets.

News of the proposed Crown Books spinoff sent the price of Dart stock soaring yesterday to around $110 after closing Thursday at $96 bid, $99 asked. A year ago, shares in the Landover-based drug chain were selling at $12.

Neither Robert Haft nor his father, Dart founder and Chairman Herbert Haft, was available for comment yesterday. Robert Hirsch, the Washington attorney who distributed the announcement, said it was premature to speculate on what percentage of Crown shares might be sold to the public, or at what price.

Dart Drug, which reported 1982 earnings of $9.1 million on sales of $291.8 million, owns half of Crown's shares. The other half is owned by Thrifty Drug, a California chain that Hirsch said also is involved in the negotiations over the planned sale.

Dart does not disclose the earnings of its subsidiaries, so it is not known how much Crown, a nationwide chain of 125 stores, contributes to Dart sales and profits. Those figures will have to be disclosed in the prospectus for any public stock sale.

Market analysts said that, if the Trak Auto pattern is followed, Dart will be able to raise millions in cash while retaining majority ownership of a subsidiary that accounts for a large share of its profits.

Kenneth Gassman, an analyst with Wheat, First Securities, said that Trak and Crown combined probably account for at least 75 percent of Dart Drug profits. Gassman said that, when Dart, which has only 1.8 million shares of stock outstanding, spun off Trak, it marketed 5.8 million shares of the subsidiary. By retaining ownership of 68 percent of them, Dart created a situation in which every $1-per-share profit at Trak returns $2.15 to Dart, he said.

Eliot Benson, director of research at Ferris & Co., said he has "never seen the books on Crown, but it's supposed to be a terrific operation."

Benson said that the run-up in the price of Dart shares reflected Dart's ownership of Trak stock. With Trak stock selling around $43, each Dart share represented $101 worth of Trak, meaning that investors in Dart at $112 could "theoretically pick up the rest of the company at $11" per share, he said. But he warned that he considers Trak overpriced, with the stock selling at 17 times earnings.

The successful spinoff of Trak and the planned sale of Crown reflect the stunning growth of the two Washington-area companies. Trak, which was founded in 1979, earned more than $4 million last year. Crown, an aggressive discounter founded by Robert Haft in 1977, is the dominant area book retailer.