Unemployment in Maryland leaped 1.7 percentage points, from 8 percent in December to 9.7 percent in January, breaking December's record high and reflecting soaring layoffs and winter's bitterest weather, the state Department of Human Resources announced yesterday.

Subzero temperatures and high layoffs among steel and auto workers left 206,748 Marylanders looking for jobs in January, an increase of 24 percent over the number idle in the same month of 1981, in which 7.8 percent of the state's labor force was out of a job.

The continued recession, reflected in national unemployment statistics of 8.8 percent and in Virginia's record 7.8 percent unemployment for the same period, weighed heavily in the Maryland count.

Workers in Washington's suburbs fared significantly better than their fellow Marylanders. Overall metropolitan D.C. unemployment for January was 5.6 percent, compared with 1981's 4.1 percent, a figure soon to be revised, the division said. Prince George's County had 6.6 percent unemployed, and Charles County had 6.2 percent.

Separate unemployment figures for the District of Columbia are due to be released by the city government today.

Montgomery County recorded the state's lowest rate--4.4 percent of its labor force was unemployed in January, compared with 3.7 percent in December. Although federal workers have been feeling the effects of this recession as never before--the Montgomery figures represent an increase of seven-tenths of a percentage point--that segment of the work force continues to be strong, said Pat Arnold, director of the Research and Analysis Division. He speculated that the consulting industry in that county, particularly defense-related, could be helping to offset layoffs among federal workers.

The other extreme exists in Somerset County, where severe weather hurt the seafood industry on the rural lower Eastern Shore and unemployment was 31.2 percent in January.