The unemployment rate for District of Columbia residents fell to 10.3 percent in January, down half a point from a revised December rate of 10.8 percent, the District's Department of Employment Services reported yesterday.

The decline may have been due to seasonal factors as many workers, including students, sought temporary jobs during the Christmas shopping season and then left the labor force, the department said. The size of the labor force fell 3,300 and employment only 1,500, so that the number of unemployed District residents dropped by 1,800 to a level of 32,400.

Total employment in the District, including jobs held by suburban commuters, dropped by 8,500 in January to a level of 585,000, with most of the decline coming in wholesale and retail trade employment. That figure is 6,400 lower than in January 1982, and 27,800 lower than in January 1981.

The decline in employment over the past year was the result of a 1,700 drop in private jobs and a 6,600 drop in federal government jobs, partially offset by a 1,900 increase in District of Columbia government jobs.

In the past two years, federal employment in the District is down by 23,500, more than a 10 percent drop. Private employment has fallen by 5,500 jobs over the same period, the department said.

For the metropolitan area as a whole, employment fell from 1,609,300 in December to 1,573,700 in January.

As in the District, most of the decline occurred at retail stores, with employment there falling by 12,300. The number of jobs in the service sector went down by 10,600.

All these figures cover full-time and part-time employes, except proprietors, self-employed workers, unpaid family workers and employes of private households.

Revised figures show that the average unemployment rate for District residents for 1982 was 10.6 percent with 33,000 persons looking for jobs but unable to find them. Monthly rates ranged from a low of 9.4 percent in January to the 10.8 percent reported for December.

The department also said that during January, 5,332 initial claims were filed for unemployment benefits under the regular unemployment insurance program, up sharply from the 3,784 filed in December.