Crown Books Corp. yesterday delayed plans to sell stock to the public after the Securities and Exchange Commission questioned the size of the profits Crown claims to have made in the last two years.

The announcement triggered a nose dive in the shares of Crown's parent company, Dart Drug Corp., which had jumped 345 percent so far this year, the biggest gain for a Washington stock.

Dart stock dropped $26 a share in heavy over-the-counter trading yesterday and closed at $117 bid and $121 asked.

Dart stock had soared from $15 a share to almost $146 in the last year because speculators were counting on the company to boom as the result of selling part of its stake in Crown and Trak Auto, two new ventures started by Robert Haft, the son of Dart founder Herbert Haft.

The company said yesterday that the SEC has ordered it to cut its quarterly profits by amounts ranging from 16 to 59 percent.

Crown said it will amend its financial statement to reflect, among other things, interest expense on bank loans. By not deducting the cost of borrowing money, Crown made its profits look larger than they actually were.

The company originally said that it would use the money raised by selling stock for expansion, but yesterday said part of the cash will go to pay off bank loans and eliminate future interest expense. Crown and Dart officials would not expand on the announcement.

Crown had been expected to begin the sale of stock this week. Investors were so eager for the stock that Crown raised the initial asking price a few days ago from a range of $19 to $23 a share to $32 to $36 a share.

The delay in the stock offering and factors contributing to it are almost certain to have an effect on the offering price, several stock market analysts agreed.

"I guess some questions will be raised about the value of the stock," said Eliot Benson, director of research at Ferris & Co. Inc. "Clearly, this is going to result in a lower price of the stock, and how much lower will depend on what else develops."

"This has got to be reflected in the offering price to some degree," agreed Kenneth Gassman, a vice president at Wheat First Securities, the big Richmond brokerage. "There is the emotional market and there is the fundamental market. Fundamentally, the stock ought to be worth less."

Gassman recalled that questions had been raised in the investment community about the real market value of another Dart Drug Corp. subsidiary, Trak Auto, which sold stock to the public in April.

Stock in the discount auto supplies chain was offered at $22 a share, but by the end of the first day of trading, Trak shares were going for more than $33 and later hit a high of $45. Yesterday, Trak fell 1 3/4 to $40 1/2 bid, $41 asked.

When the price of Trak stock was soaring, Dart Drug shares soared alongside them. Because Dart Drug owns 71 percent of Trak Auto, every time the price of Trak stock increased, the value of Dart's investment in Trak increased and the value of Dart stock went up again.

The same effect pushed the stock of Dart still higher after the company announced that it would sell shares of Crown to the public, but would retain controlling interest.

The factors that pushed the stock up 900 percent in the last 12 months also could work against the companies. Said Gassman: "Now we have a shadow cast on the organization--Dart, Trak and Crown--and that's got to hurt the price-earnings multiple and market receptivity of the Crown issue."

Trak and Crown together produced more than 70 percent of Dart's total profits last year.

But some analysts questioned Trak's earnings and value as well as expenses because the company shares warehouse space and distribution systems with Dart.

Crown estimated yesterday that a restatement of its financial results will reduce net income by $302,000, or 18 percent, for the fiscal year that ended Jan. 31, 1982, and by $593,000, or 20 percent, for the succeeding year. Net income will be reduced by $163,000, or 59 percent, for the three months ended April 30, 1982, and by $126,000, or 16 percent, for the quarter which ended April 30, 1983.

The original registration statement that Crown filed at the SEC reported net income of $1.7 million (31 cents a share) for the fiscal year ended Jan. 31, 1982. The company reported net income of $2.9 million (53 cents) for the year ended Jan. 31, 1983.