Commerce Secretary Wilbur Ross, who oversees the Census Bureau, has said he ordered the citizenship question added to the census because the Justice Department needed citizenship data to better enforce the Voting Rights Act. But judges in three federal lawsuits opposing the question, including Judge Hazel, have called that a poorly manufactured excuse that conceals a different motivation.

Plaintiffs in the lawsuits — cities, states, advocacy groups and others — say Mr. Ross is trying to turn the census into a political weapon against Democrats. They say the citizenship question will deter noncitizens and minorities from filling out the form, leading to an undercount in the predominantly Democratic areas where they live. And they charge that the Republican Party wants a count of noncitizens so that it can exclude them entirely from the population base used for drawing new political maps.

By that argument, the citizenship question is an extension of the Republican Party’s wildly successful effort in 2010 to gain and hold political power by controlling the redistricting process. The strategy then was to pour money and talent into winning control of the state legislatures that draw political maps.

The strategy now, the plaintiffs say, is to further control redistricting by reducing the number of people who are represented in Democratic districts — and thus reduce the number of Democratic districts as well.

The Trump administration has dismissed that as fantasy. But evidence from the lawsuits showed that Mr. Ross took an interest in the impact of noncitizens on political maps only weeks after taking office and invented the rationale that more data was needed for Voting Rights Act enforcement.

The disclosure of Mr. Hofeller’s files last month added weight to the plaintiffs’ claims. They included a study that Mr. Hofeller prepared for a major Republican donor in 2015, which concluded that the next round of redistricting could be swayed to Republicans’ advantage in some states by excluding mostly Hispanic noncitizens and people under voting age from the population totals used to draw political maps. But that could only happen, he wrote, if the next census included a question on citizenship.

The next year, Mr. Hofeller urged President-elect Trump’s transition advisers to add the question to the 2020 census.