A rising number of trade associations are relocating from New York to Washington, according to data recently published by Columbia Books Inc. in its 1981 compilation of national labor unions and trade and professional associations in the United States and Canada.

Washington has been the site of choice for associations since 1975, due primarily to the presence of the federal government and national and trade media, the Columbia Books statistics show. In 1981, the city hosted 29 percent of the listed U.S. trade and professional organizations, up from 28 percent in 1980. New York City dropped a point to 20 percent, and Chicago moved up slightly to 15 percent.

But the study revealed another trend that is a bad sign for the District: When national associations move into the area, they are likely to settle first in downtown Washington. After several years in the city, however, they tend to relocate again, this time to the suburbs. Fairfax County has been a major beneficiary of this secondary trend, with associations based in Fairfax jumping 11 percent in 1981, from 159 to 176.

The Columbia Books data attributes the relocations into Fairfax County to cost, particularly corporate leasing rates. Office rents for new construction in downtown Washington are now projected to reach $30 a square foot by mid-1982, according to a recent Coldwell Banker survey. Comparable space in Fairfax County will range from $14 to $18 during the same period. Other factors favoring Fairfax County include utility expenses, parking costs and availability.