Maryland's unemployment rate dropped in October for the third consecutive month, partly because of increased hiring in schools and the construction industry, state officials said yesterday.

For the state as a whole, the number of jobless dropped by about 2,500 persons, or a tenth of a percent, to 8 percent. This was 0.9 percent above the October 1981 rate.

Last month there were 174,072 people in the state without jobs. Those employed totaled 2,007,331, according to the Maryland Department of Human Resources. Spokesman Luther Starnes attributed the gain in the number of people who had found jobs to increased school staffing and to lower interest rates, which stimulated the building and trucking industries.

Montgomery County posted the lowest unemployment rate in Maryland: 4 percent. And in the Maryland suburbs of the District as a whole, unemployment dipped from 5 percent to 4.8 percent in October.

The highest unemployment rate was 16.9 percent in Garrett County, on the West Virginia border. Baltimore's jobless rate dipped to11.2 percent, or three-tenths of a percent lower than in September, while the Baltimore metropolitan area showed a decline of the same size to 9.4 percent.

Starnes noted that Maryland's slowing unemployment rate runs counter to the national trend.

Comparable national unemployment figures for October (not adjusted for seasonal factors, just as the state figures are not adjusted) put unemployment at 9.9 percent. An increase is expected when the national figures for November are released today.