Washington's unemployment rate declined slightly in April to 10.3 percent from 10.4 percent in March, while the metropolitan area's unemployment rate fell from 5.4 percent to 4.9 percent, the District's Department of Employment Services reported yesterday.

Employment Services Director Matthew F. Shannon said that federal employment in the metropolitan area grew by 1,300 over the last year, the first time it has risen in year-to-year monthly comparisons since January 1981.

In January 1981, Ronald Reagan was sworn in as president and vowed to reduce federal payrolls as part of an overall program to cut federal spending. Most of the new federal jobs were in the suburbs.

The nationwide unemployment rate in April was 10.2 percent, and yesterday the Department of Labor reported that it fell to 10.1 percent in May.

However, when the District's unemployment rate is adjusted for normal seasonal variations--as the nationwide figures are--the unemployment rate in Washington rose from 10.3 percent in March to 10.8 percent in April. The government does not report a seasonally adjusted unemployment rate for the metropolitan area.

Shannon said that the increase in employment and reduction in the area's unemployment rate is due to an improved economy, but cautioned that many of the gains may be seasonal, "since there have not yet been signs of a sustained cyclical upswing in the area's labor market growth."

Economists often seasonally adjust unemployment data in order to separate ups and downs in hiring and job-seeking trends that occur at the same time each year from more fundamental changes in employment. For example, the unadjusted unemployment rate almost always falls sharply in December because of holiday hiring and usually rises sharply in May when students flood the job market.

Shannon said the number of unemployed District residents fell to 32,500 in April from 32,700 in March. In April 1982, however, only 31,000 Washington residents were out of a job and looking for one.

The number of Washington residents with a job rose to 284,000 in April from 281,900 in March. There were 2,200 more jobholders in Washington in April than in April 1982. However, the total labor force--those with a job and those actively searching for one--grew by 3,600 over the year. As a result, the April 1982 unemployment rate, at 9.9 percent, was lower than the 10.3 percent reported for April 1983.