Maryland's unemployment problems showed some signs of easing in January, the state's Department of Human Resources reported yesterday.

Joblessness increased by 0.7 percentage point from December to January to 9.1 percent. The increase was only half the size of those registered between December and January in 1982 and 1981.

"We are relatively optimistic that we might be coming into a recovery period," said Curtis Kane, a spokesman for the department, which gathers the figures.

The percentage of jobless workers in January 1982 was 9.4 percent.

State officials noted that, after four months of decline, manufacturing employment in January reached the lowest level since 1941. At the same time, however, job losses in manufacturing, ship and boat building, and repair and food processing were less extensive this January than in the same month the previous year. Only the declines in trade and federal government employment were greater than in January 1982.

There were also layoffs in the trucking industry, water transportation, educational institutions, hotels and lodging places, amusement and recreation facilities, agricultural services and business services. Some of those layoffs are seasonal.

Lower interest rates and moderate weather held seasonal layoffs in construction work to about half the level of such layoffs last winter.

The highest unemployment rate--26.7 percent--was in Somerset County, while the lowest--4.1 percent--was in Montgomery County, up from 3.7 percent in December.

The overall rate for the Maryland suburbs of D.C. was 5 percent, up from 4.6 percent in January. Rates were 5.8 percent in Prince George's County, up from 5.4 percent; 5.5 percent in Charles County, up from 4.5 percent; and 5.8 percent in Howard County, up from 5.7 percent.