Alaska, reaping the riches from oil and mineral production, led the states in per capita personal income last year, while Mississippi ranked last, new Commerce Department figures show.

Alaskans earned an average of $13,763 for each resident in 1981, outpacing the District of Columbia, where per capita income was $13,539, and Connecticut, the second-ranking state at $12,816.

Maryland, with per capita income of $11,477, was somewhat above the national average, while Virginia was just below the average with $10,349.

Alaska, which also finished first in 1980, is collecting such substantial revenues from its huge oil pipeline that the state was able to send $1,000 royalty checks this year to every citizen.

The fastest rising state in per capita income by far was rural North Dakota, whose $10,213 figure brought it from 35th to 25th among the states, a 23.4 percent increase over 1980. By contrast, the nation's per capita income increased 10.7 percent, which brought with it an a modest increase in purchasing power over last year's 8.5 percent inflation.

Most of the big gainers, led by North Dakota, South Dakota (up 14.5 percent) and Nebraska (up 15.9 percent), recorded large increases in farm income last year.

States showing the slowest growth in income had sizable population increases last year, but not much increase in earnings from manufacturing or other industries. These include Michigan, Ohio and Wisconsin (up only 7.8 percent).

Mississippi had the lowest per capita income, $7,408, edging out South Carolina for last place.