Government Employees Insurance Co. continued a recent string of "good news" announcements yesterday, revealing that automobile insurance rates in the District have been sliced an average 3.7 per cent.

The insurance firm, which was on the threshhold of failure 18 months ago, had already reported in recent weeks a continued increase in profitability, a resumption of cash dividends on common stock and a rate reduction for customers in Virginia.

The D.C. rate cut took effect Monday for policy renewals and new customers. Geico, based in Chevy Chase, is the largest insurer to private autos in the city with about 45,000 customers.

Company officials said the reduction was possible because of a decreased frequency of claims for Geico-insured cars.

According to spokesman Robert W. Jackson, an average two-car District family with a 1977 Chevrolet Impala used for daily commuting and a 1974 Ford Mustang used only for pleasure trips, now pays $551.10 a year for standard coverage limits recommended by the firm.

Under the new rates approved by the D.C. Insurance Department, the same family would pay $530.30 a year - a reduction of $20.80 or $3.78 per cent. Average customers will get a $17 decrease, depending on numbers of vehicles and extent of coverage, the Geico spokesman said.

Jackson said Virginia and the District are the only two jurisdictions where Geico has reduced rates in general. But he said the company is monitoring rates and claims frequency in Maryland and other states and could make periodic adjustments in the future.

He said also that the company is working on developing a policy of announcing to the public all future rate increases or reductions, a policy followed by industry giant State Farm. Previously, Geico rate adjustments were filed with regulatory agencies but no announced to the general public.

In Virginia, Geico last month reduced premiums by an average of 5 per cent. With 135,000 policies in force, Geico is the state's second-largest auto insurer.