Lawyers for the District sued the U.S. Census Bureau in federal court yesterday, alleging that the bureau's policy of counting the 7,000 inmates of the Lorton Correctional Complex as Virginia residents could cost the District as much as $60 million in federal funding over the next decade.

The lawsuit is the fifth legal challenge to the 1990 Census, bringing to more than 20 the number of cities, states or counties that say the Census Bureau is undercounting people in their jurisdictions, said Catherine Miller, chief of the Commerce Department's program and policy office.

At the same time, Acting Corporation Counsel John Payton said that the District will join another lawsuit charging the Census Bureau with using statistical techniques that result in undercounting minorities. That lawsuit, filed in 1988 by New York City, also includes as plaintiffs California and Texas, as well as Houston, Los Angeles and Dade County, Fla.

"The financial impact of the census's undercounting is very serious," Payton said in a statement released yesterday. Because federal grants are allocated on the basis of population count, he said, "the District will lose tens of millions in dollars unless these actions are remedied."

The lawsuit filed yesterday in federal court here challenges the definition of Lorton as a part of Virginia.

Normally, Miller said, the Census Bureau counts people according to their "usual residence." Because Lorton inmates are, by definition, people who never leave Virginia, the bureau counts them as Virginia residents.

The District's lawsuit argues that because Lorton sits on federally owned land, and the District pays the entire bill for the upkeep of all the inmates there, that technically makes the inmates residents of the District.

Claude Bailey, a spokesman for the D.C. Corporation Counsel's Office, said yesterday the lawsuit is aimed at counting only Lorton inmates who were D.C. residents before they were sent to Lorton. The prison is made up of people who committed crimes in the District, including people who lived outside it when they were convicted.

The prisoner-counting issue is not new. In August, then-Del. Walter E. Fauntroy (D-D.C.) introduced a bill in Congress that would have defined Lorton as a piece of the District in exile. The bill went nowhere.

In addition, Miller said that the issue had been raised in previous census counts by other states or cities that housed prisoners outside their political boundaries. She said she could recall no case involving that issue reaching the courts.