The District of Columbia will suffer the greatest per capita loss of federal assistance in the country as a result of federal cutbacks in domestic programs, according to a new state-by-state analysis released yesterday by two labor groups.

The report's findings, which were immediately questioned by D.C. government officials, suggested that the District will lose a total of $851 million in direct federal aid by 1984 because of policy changes ordered by President Reagan shortly after he took office.

The District led the nation in per capita losses of federal assistance for 11 programs, according to the report, including handicapped education, vocational education, health services, social services, subsidized housing, urban mass transit and community development block grants.

"The District of Columbia is among the states with the highest level of participation in federal aid programs," said David C. Wilhelm, a research director with the AFL-CIO. "When cuts are made, they suffer the greatest per capita losses."

The report, entitled "State of the States," was prepared by the American Federation of State, County and Municipal Employees (AFSCME) and the AFL-CIO's Public Employees Department. The study indicated that state and local governments would lose a total of about $57 billion in federal aid between fiscal years 1982 and 1984 as a result of the policy changes.

City budget experts, while acknowledging serious problems resulting from cutbacks in federal aid, said the new report's projections may have greatly exaggerated the impact on the District.

"I think this is overstating the case," said Diana Carsey, a D.C. budget official who oversees federal grants. "It's a worst-case, oh-my-god-look-at-what-they're-doing-to-us analysis. Their numbers are being projected from Reagan policy changes but they don't appear to acknowledge new programs that came in to take the place of some that were cut."

Gladys W. Mack, the mayor's director of policy and program evaluation, added: "I would wonder if there aren't some statistical quirks in there."

Direct federal assistance to the District declined by only $13 million between fiscal 1981 and 1982, according to city figures, from $380 million to $367.8 million.

Yet the labor report concluded that the city actually lost $204 million in federal aid in fiscal 1982, by comparing what the city received under Reagan's revised budget with what former President Jimmy Carter had proposed to provide before he left office.

Similarly, the report projected that the District would have received $281 million more in federal aid in fiscal 1983 and $366 million more in 1984 if Carter's budget policies hadn't been reversed by Reagan.

"We are defining budget cuts in different ways than the city," explained Wilhelm of the AFL-CIO. "They are looking at current dollars, year to year. But that kind of analysis does not reflect the full impact of policy changes. . . . You must look at it in terms of what you would have needed in budget increases to maintain the current level of services."

District officials say they anticipate receiving a total of $387 million in federal assistance in fiscal 1983, the current year, and $388 million in fiscal 1984.