More than two-thirds of the city's residential properties have been assessed inaccurately by the D.C. government, with many overassessments occuring in low- and moderate-income neighborhoods where residents are less likely to complain, according to a report released yesterday by a coalition of neighborhood and public interest groups.

In the report, which follows the city's announcement Friday of an average increase of 21 percent in residential property values, Citizens for Fair Assessment contended that the value of 39 percent of the residences in the city have been overestimated, with most of these errors occurring in low- to moderate-income neighborhoods including Old City 1 (Near Northeast and Southeast), Anacostia, Deanwood and LeDroit Park.

About 31 percent of the city's homes were underassessed and 30 percent fairly assessed, the report says, adding that many of the underassessments were made in neighborhoods of generally more expensive homes.

Luis Zapata, a coalition spokesman and community organizer representing residents of Southeast Washington, said an average of 19 percent of the homes in Old City 1, and 18 percent of the homes in Anacostia are overassessed.

"The assessors refuse to admit that their package is unreasonable, or they say there are reasons but then they are unable to explain them. Basically, they tend not to find their own mistakes. The same pattern emerges with the Board of Equalization and Review when people attempt an appeal. They are tremendously unresponsive.

"People don't appeal because they are afraid their own assessments will increase. This doesn't happen often, but the board does nothing to dispel that notion. They don't want any more business than they already have," he said.

Carolyn L. Smith, director of the D.C. Department of Finance and Revenue, said yesterday that the group had not provided her office with a copy of the report, despite several requests that they do so. She said she doubted the group's findings. The assessments are "99 percent correct," she said.

"We included a booklet explaining the assessment procedure in all of the notices that were just mailed," Smith said, "and we encourage people to discuss any problems they may have with the particular assessor who looked at their property.

"We explained in the booklet that this would have no effect on the assessment, and if we do find an error, we would encourage and assist anyone in making an appeal."

Property assessments are based primarily on external visual inspection and on the sale prices of homes in each of the District's neighborhoods during the first year of what is approximately a three-year taxation cycle. Thus, current assessments would be based on 1979 property values.

Zapata said the result of the inaccurate assessments is that people who can least afford it -- those of low, moderate, and fixed incomes -- ultimately pay an unfair proportion of the city's property taxes.

He said the District's tax assessors have not been properly trained in estimating property values, and use no uniform code in doing so. "In poor neighborhoods, they [the assessors] have a tendency to say, 'I will not be as accurate,' and to a great extent they make this decision because poor people don't have a lot of political muscle."

The organization's report claims that more than 50 percent of the homes in the Garfield, Wesley Heights, Central, and RLA Southwest assessment districts were underassessed based on 1979 property sales figures.

Zapata said the organization favors a uniform assessment procedure in the city, and, in neighborhoods with a high percentage of overassessments, the right to appeal on a class-action basis.

According to the latest figures, the greatest increases in property values took place in two older neighborhoods on the northwest fringes of downtown -- Kalorama, with a 39.3 percent rise, and Mount Pleasant with an average increase of 37.1 percent. The smallest increases were in Randle Heights, Deanwood, and Hillcrest, all east of the Anacostia River, with rises of 5.3, 5.4, and 5.6, percent respectively. Coalition members say it is possible for most homes in a neighborhood to be overvalued even when the overall neighborhood assessment increase is small.