The legality of at-large voting systems is being challenged in other cities, including Pasadena, Tex., and Yakima, Wash. The suits contend that at-large systems violate Section 2 of the Voting Rights Act, which prohibits voting practices or procedures that discriminate on various factors, including race.

Many challenges of at-large voting have come in places where whites are the clear majority. But in the Ferguson-Florissant district, the population is almost evenly divided, according to the most recent census data. Courts have not definitively ruled whether a violation of Section 2 is possible in places where blacks might not be in the minority, said Richard L. Hasen, a professor of law and political science at the University of California, Irvine.

The case “raises legal questions over whether, if it’s true that African-Americans make up a majority of the relevant population, whether a Section 2 remedy is possible,” he said.

Whether blacks outnumber whites in the district is in dispute. The A.C.L.U., using 2010 census data, contends blacks make up 48.19 percent of the voting-age population in the district, which is less than whites. The district, using 2013 American Community Survey data, asserts that blacks, at 48.94 percent, represent a slightly higher share of the voting-age population than whites.