Dart Drug Corp. disclosed yesterday it is preparing to spin off part of its Trak Auto stores chain by selling shares in Trak Auto to the public.

A Dart official said the company has held preliminary negotiations for a public offering of Trak Auto shares.

The spokesman emphasized that plans for the offering are still tentative, but he said the company probably would form a separate Trak Auto corporation in which Dart would remain a major stockholder.

Proceeds from a public offering would be used to finance expansion of Trak Auto, which was founded in 1979, said Charles Shipe, vice president of Dart Drug Corp.

The offering of Trak stock could be made within 60 to 90 days, although no decision has been made, Shipe said.

Dart Drug, a Landover-based company, formed an affiliate last year to operate Trak Auto stores in California and sold a half interest in the new corporation to Thrifty Corp. Thrifty, a West Coast drug chain, already owned a 50 percent share of the Crown Books chain, another Dart spinoff. The first of 10 Trak Auto stores in the West Coast division will open about 45 days from now.

The Trak Auto chain on the East Coast has expanded to 46 stores in just three years.

Dart does not report separate sales or profit information for Trak or Crown Books. The entire corporation--including Trak, Dart's share of Crown Books and the chain of 65 drug stores--reported sales of $209 million and net income of $2.63 million for the nine months ending Oct. 31, 1982, compared with sales of $198 million and earnings totaling $1.7 million in the comparable nine-month period in 1981.