Mid-June sales of new American-produced cars were the worst for the period in almost a quarter of a century, skidding 22.4 percent below their level for 1981, surprising some analysts, who had seen the strong showings for May and the first 10 days of June as a signal that the three-year slump was coming to an end.

Meanwhile, GM Chairman Roger Smith said yesterday that he expects to clinch a deal some time this fall to produce subcompact autos in the United States with the Japanese automaker Toyota.

And Chrysler said it is offering rebates of between $300 and $1,000 on 1981 and 1982 pickup trucks through July 31.

There were 118,095 American-made new cars sold from June 11 to June 20 compared with 171,196 during the middle 10 days of June 1981, and the sales rate of 14,762 cars a day was the worst since the same period of 1958, when the daily rate was 14,650 cars, sales data released yesterday indicated.

So far this year, sales are 11 percent lower than last year at this time at 2.77 million cars.

General Motors Corp.'s sales for the 10 days fell 25 1/2 percent from last year's levels to 68,498 cars, Ford Motor Co.'s were 16.8 percent lower at 30,781 cars, Chrysler Corp.'s were off 14 percent at 14,734, American Motors Corp.'s were estimated as down 37 1/2 percent at 1,900, and Volkswagen of America's declined 31 1/2 percent to 2,182.