While most economic indicators show the nation plunging into a sharp recession, with unemployment climbing rapidly, the number of out-of-work residents in the recession-resistant Washington area is declining.

The unemployment rate in the Washington area dropped from 4 percent in March to 3.8 percent in April. In the District of Columbia, where unemployment is usually higher, the rate also declined, from 6.6 percent to 6 percent.

The latest unemployment statistics show once again that the Washington area, with its economy rooted in the federal government's massive payroll and the jobs that exist here because of the government, is virtually immune to some of the economic factors that are causing hardships elsewhere.

"I don't know if we're recession-proof, but D.C. and the Metro area don't track the nation like some areas do," said city government statistician Lawrence Thurston. "If you look at Michigan, some parts of California, Ohio, or Pittsburgh, you'll see quite a different thing happening.

"The nation is in a recession, but the District of Columbia is quite dissimilar from the nation. The industry base [the federal government, not manufacturing] is quite different."

The figures show almost every category of employment either holding steady or increasing slightly in the number of jobs from March to April throughout the Washington area.The largest increase in any job category occurred in the city, which added an additional 800 service jobs, chiefly hotel and restaurant positions.

The one exception to the trend was in state and local government, which showed a slight decrease in the number of jobs between March and April. The federal job picture remained steady.

Rufus Daniels, Chief of the D.C. Manpower Research Center, said, "When you're talking about the District of Columbia, the economic base is entirely different. The nation has a production-oriented economy. Most of the layoffs you see [nationwide] have been in manufacturing -- the auto industry, specifically."

The April figures, the latest available statistics on the Washington area's economic health, show a continuation of a trend: The unemployment rate has been dropping here and rising nationally. Unemployment in the District for April, 1979, was up to 7.0 percent and was 4.2 percent for the entire metropolitan area, including Washington and its Maryland and Virginia suburbs.

The District had 23,000 workers without jobs in April, 1979. But by last April, the number of unemployed D.C. workers had dropped to 18,700 and 3,000 jobs had been added, according to city government statistics. Total employment in the city increased over that one-year period from 293,100 to 294,700.

"I am heartened by these new figures," said William R. Ford, director of the D.C. employment services office. "The positive impact of 3,000 job increase in one year has to be felt in the community. We plan to continue our efforts to encourage business development and the hiring of D.C. residents. This is just a beginning."

There were no new joblesss figures released by the city on the number of unemployed black teen-agers. The latest available figure showed that youth unemployment is officially 29 percent, although the Washington Urban League says the figure is probably closer to 60 percent.

By contrast, national figures from the Labor Department show a 7.8 percent unemployment rate in May, compared to 7 percent in April. The March rate was 6.2 percent. The May rate for the Washington area will be released next month.

There were 3,700 fewer unemployment workers in the Washington metropolitan area between March and April this year, a drop from 63,800 to 60,100. A year ago April, there were 66,400 jobless residents in the Washington area.

The region's labor force has been steadily increasing during the past 18 months, according to the new statistics. The civilian work force for the metropolitan area in April was 1,595,700 up from 1,592,000 in March and 1,575,400 in April, 1979.