“While the court is unable to determine — based on the existing record, at least — what Secretary Ross’s real reasons for adding the citizenship question were, it does find, by a preponderance of the evidence, that promoting enforcement of the” Voting Rights Act, or V.R.A., “was not his real reason for the decision,” Judge Furman wrote. “Instead, the court finds that the V.R.A. was a post hoc rationale for a decision that the secretary had already made for other reasons.”

Judge Furman had called for Mr. Ross to be questioned under oath, but the Supreme Court blocked that order in October. Justice Neil M. Gorsuch, joined by Justice Clarence Thomas, said the court should have gone further, shutting down all pretrial fact-gathering in the census case. Justice Gorsuch added that there was no indication of bad faith in Mr. Ross’s conduct.

“There’s nothing unusual about a new cabinet secretary coming to office inclined to favor a different policy direction, soliciting support from other agencies to bolster his views, disagreeing with staff or cutting through red tape,” Justice Gorsuch wrote at the time. “Of course, some people may disagree with the policy and process. But until now, at least, this much has never been thought enough to justify a claim of bad faith and launch an inquisition into a cabinet secretary’s motives.”

In November, the Supreme Court rejected a request from the Trump administration to halt the trial, over the dissents of Justices Thomas, Gorsuch and Samuel A. Alito Jr.

In his ruling last month, Judge Furman relied on evidence in the so-called administrative record, meaning the materials the government said Mr. Ross had considered before making his decision.

Evidence presented at the trial showed that Mr. Ross had wanted to add the question long before the request from the Justice Department. The letter from the Justice Department, Judge Furman wrote, was an attempt “to launder their request through another agency — that is, to obtain cover for a decision that they had already made.”

Documents disclosed in the case showed that Mr. Ross had discussed the citizenship issue early in his tenure with Stephen K. Bannon, the former White House chief strategist and an architect of the Trump administration’s tough policies against immigrants, and that Mr. Ross had met at Mr. Bannon’s direction with Kris Kobach, the former Kansas secretary of state and a vehement opponent of unlawful immigration.