Challenges to the citizenship question are now before the Supreme Court, which is expected to issue a final ruling before the court’s term ends later this month. In arguments before the court in April, conservative justices seemed ready to accept the Trump administration’s argument that it had both the discretion and a sound reason to measure citizenship in 2020.

Late Wednesday, plaintiffs in the main census lawsuit asked the Supreme Court to allow further discovery of any remaining evidence in Mr. Hofeller’s backup drives before it issues a ruling in the case.

Experts say that adding a citizenship question would deter immigrants and minority residents from responding to the census, leading to an undercount in the predominantly Democratic areas where the bulk of them live. In addition, a census that reveals with precision where noncitizens live is crucial to plans by some conservatives to base political districts not on total population, but on the number of voting-age citizens. That, too, would benefit Republicans, particularly in states like Texas and California with large numbers of foreign-born residents.

Suspicions that an ulterior motive lay beneath Mr. Ross’s decision have been further bolstered by the way that decision was made — almost totally in secret and without testing of its language, in contrast to the years of surveys and consultation that have preceded every previous change in the census questionnaire.

Terri Ann Lowenthal, a consultant on census matters who managed the issue for the Obama transition team in 2008, said that virtually everything about the administration’s handling of the citizenship question “raised significant alarm bells.”

“The traditional process for determining census questions is done primarily in the public arena,” she said. “And that simply did not happen this time.”

When Mr. Ross announced his decision to add a question on citizenship to the census, he cast it as the culmination of months of intensive research by Census Bureau experts and advice from members of Congress, businesses and interest groups with a stake in an accurate head count and the public.