In their Supreme Court brief, Arkansas officials listed other kinds of contraband that might be hidden in beards: needles, pieces of wire, broken glass, gum, caulk, tobacco, marijuana and powdered drugs. The officials told the justices that they should not be required to produce evidence that prisoners actually used beards as hiding places.

Image Gregory Holt Credit... Arkansas Department of Corrections

“Courts should not insist on studies, data or concrete examples,” the brief said. Prisons are dangerous places, it said, and the judgments of those in charge are entitled to deference.

The state’s brief did provide one example, based on testimony last year from Ray Hobbs, the director of the state’s corrections department and the lead defendant in Mr. Holt’s lawsuit. The testimony came in a hearing concerning a different prisoner who sought to grow a beard for religious reasons.

Asked whether he knew of prisoners who “got caught concealing contraband within their beards,” Mr. Hobbs described an incident the month before. “An inmate fresh out of county jail,” he said, “concealed a part of a razor blade and later on that night committed suicide with it.”

The state’s Supreme Court brief, filed in July, cited that testimony. But it was only partly true.

An inmate named Steven Oldham did kill himself with a razor on Aug. 8, 2013, in Malvern, Ark. But he did so, according to a sworn statement from the coroner, by using “an orange plastic disposable razor” that had been issued to him by prison authorities so he could shave his beard.

Douglas Laycock, one of Mr. Holt’s lawyers, said Supreme Court briefs should meet a higher standard of factual accuracy. “This kind of flat misrepresentation to the court, however it happened,” he said, “doesn’t happen very often.”

A reply brief from Mr. Holt pointed out the error, and lawyers from the state attorney general’s office promptly wrote a letter to the court disavowing their earlier account of the incident. “The testimony of Director Hobbs” concerning Mr. Oldham, they wrote to the Supreme Court, “was erroneous in stating that the razor was concealed in a beard.”