The domestic auto industry remained mired in a deep slump, with July sales down 8.3 percent below the recession levels of a year ago.

The U.S. auto companies yesterday reprted sales of 497,151 cars in July compared with 542,349 a year ago, with Chrysler Corp. the only one of the Big 3 to improve its sales figures over the July 1980 levels.

Chrysler sold 58,508 cars last month, up 15.9 percent from July 1980. General Motors ycorp., with sales of 304,135 cars last month, was down 12.5 percent, while Ford Motor Co. sold 109,031, down 5 percent from the same month a year ago.

American Motors Corp. reported sales of 12,755 cars last month, 21.8 percent more than July 1980. Volkswagen of America also sold 12,755 of its U.S.-built models, a drop of 32.8 percent from a year ago.

The sales recovery that the industry expected two months ago still has not materialized, and GM, Ford and Chrysler have been forced to reinstate costly "incentive" programs of various kinds to attract car buyers and reduce the huge backlogs of unsold cars before new models are introduced in September. As of June 30, there were enough new domestic cars in stock and in dealers' hands to last 84 days at prevailing sales rates.

Imported cars held their ground, taking 29.4 percent of the U.S. market despite the Reagan administration limits on Japanese imports. The steep drop in the value of foreign currencies compared to the dollar in recent months has lowered the price of imported cars in this country, helping offset the limits on Japanese imports and boosting the sales of European companies such as Pergeot and BMW to record levels. Toyota was done 13.6 percent with sales of 51,006 and Datsun dropped 22.5 percent with 43,118 cars sold in July.

The July sales results for American auto companies were an improvement over June, when the market sank to the lowest level for that month in 23 years. Taking seasonal adjustments into account, domestic car sales in July reached an annual rate of 6.1 millin units compared with 5.5 million in June, a rate too low to permit the companies to recover from last year's losses.

In actual sales, only Chrysler advanced between June and July, with an increase of a mere 54 cars. Ford's July sales were 10,931 less than the June figure, and GM was off 6,751 car.

The final 10-day sales period in July did not improve the picture for the domestic industry. Sales totaled 207,890, down 11 1/2 percent from the same period a year ago. GM's sales wee off 21 percent, Ford's rose 14.7 percent, Chrysler gained 10.2 pecent, AMC was up 87.8 percent over its disastrous results of a year ago and Volkswagen was down 38.2 percent.

For the first seven months of 1981, the U.S. auto companies sold 3.895 million cars, down 2.9 percent from last year's total at this time whe the industry was on its way to an $8 billion pretax loss in the North American market.

Heavy cost-cutting, deferred investments and a heavy spring construction scheduled enabled the Big 3 to report profits for the second quarter, but the balance of the year looks grim unless a psychological impact of the new tax bill revives the auto market, analysts say.

In his August forecast, Otto Eckstein of Data Resources Inc. said that with the economy stalled by high real rates of interest, the outlook for auto sales is not good. His analysis shows sales declining slightly during the second half of 1981 at an annual rate of 6.3 million cars. In a good year, the rate would be above 8 million units.

Townsend-Greenspan & Co. said in a July 31 letter to investment clients that auto companies may have to slow production of 1982 models this fall and even delay some model introductions.