The University of the District of Columbia's board of trustees voted last night to raise nonresident tuition costs by nearly one third, to $2,100 a year, beginning this fall.

The increase, covering undergraduate and graduate students from out of state, will affect about 14 percent of the university's 14,107-member student body, according to John H. Britton Jr., university spokesman. He said the 11 board members who attended the meeting voted 9 to 1 in favor of the increase with one member abstaining.

Britton said he knew of no planned changes in tuition charges for District residents, which are now $330 a year for undergraduate students and $777 for graduate students. UDC last raised those rates in the fall of 1981. The current tuition for out-of-state students is $1,580 for undergraduates and $1,587 for graduate students.

The board's resolution must be published in the D.C. Register and after a 30-day comment period, the board must take a final vote.

Among other area schools, tuition at the University of Maryland will go up 13 percent in the fall, to $1,128 for Maryland residents and $3,523 for students from out of the state, and George Washington University's undergraduate tuition will climb to $6,100, a 24.5 percent jump.

Tuition at GWU's medical school will drop by $250 this fall, to $18,750 a year.