Plans for a 12-story, $10-million office building in downtown Columbia were announced this week.

K & M Development Corp. Inc., a new firm based in its own small building in Columbia, reported that construction will begin this spring on a structure to be named for the principal tenant, Columbia Bank & Trust Co. The 1.4-acre site is adjacent to the big Columbia Mall and the pedestrian bridge over Little Patuxent Parkway.

Co-developer Patrick McCuen said that the bridge connecting the mall and the lake area will pass through the new building's lobby.

K & M's other principal, Peter Kirk, said that Hamilton Murphy Garrison of Bala Cynwyd, Pa., designed the building that will be built by Leimbach Construction of Baltimore. W. C. Pinkard & Co. is the leasing agent. Office space, nearly one-third of which is preleased, will be available in a range between $12 and $14 a square foot.

Columbia, a new town started on 15,000 Howard County acres in 1967, now has nearly 60,000 residents in the community midway between Washington and Baltimore. In recent years millions of square feet of new office, commercial and light industrial space have been built and occupied in the community located on Rte. 29 in Howard County.

The highest existing building in Columbia is American Cities but a 10-story addition is under way on the Cross Keys Inn. The new Columbia Bank building is expected to be completed late in 1982.