SAN FRANCISCO — Asian-Americans have been the fastest-growing minority group in the legal profession for the past three decades, but they’ve made only limited progress in reaching the upper echelons of the law, according to a study released Tuesday.

A Portrait of Asian Americans in the Law,” published by the National Asian Pacific American Bar Association and Yale Law School, reports there are over 50,000 Asian-American lawyers in the United States today compared to 20,000 in 2000. The study, billed as the first comprehensive look at the career paths of Asian-American law students and lawyers in the United States, found that Asian-Americans account for nearly 5 percent of lawyers and about 7 percent of law school students nationwide—as compared to 6 percent of the entire population.