“We know this question is going to have a detrimental impact on our efforts and is going to make people wary of responding,” said Erika Reyna, who is coordinating census efforts in Hidalgo County in southern Texas — in part because she and others determined that the Hispanic population had been undercounted in the state in 2000 and 2010.

“An undercount will mean fewer resources in an area that is high-need and growing,” Ms. Reyna said.

She said the county is in sore need of funding for education, transportation, health and other services.

The question about citizenship could have a disproportionate impact on the count in red states, like Georgia, where the Latino population is relatively new, skews undocumented and is largely Spanish speaking. In the 1990s, immigrants flocked to fast-growing Atlanta to build homes, work in restaurants and perform other, low-skilled work.

The state’s one million Latinos now account for about 9 percent of Georgia’s population. About a third of them are undocumented immigrants, many of them parents to children born in the United States who could be undercounted, according to the Georgia Association of Latino Elected Officials.

“We have many mixed-status families, and given this administration’s record on being anti-immigrant and Latino, the question will sow fear and confusion,” said Jerry Gonzalez, executive director of the association.

A coalition of state attorneys general advised the Commerce Department last month against including the citizenship question, saying that in addition to undermining participation among immigrants, it would result in an undercount of the overall population in many areas. The state of California has already filed suit, arguing that including the question is a violation of the United States Constitution, and Attorney General Eric Schneiderman of New York announced he would lead a separate multistate legal challenge.

The decennial census influences political representation in Congress and federal funding for an assortment of programs. The Commerce Department says that between 1820 and 1950, almost every decennial census asked a question on citizenship in some form.