WASHINGTON — The Supreme Court on Thursday turned down a request from Idaho prison officials to block court-ordered sex reassignment surgery for a transgender prisoner.

The court’s brief order, which gave no reasons, let stand a ruling from the United States Court of Appeals for the Ninth Circuit, in San Francisco, in favor of the prisoner, Adree Edmo, a transgender woman.

Justices Clarence Thomas and Samuel A. Alito Jr. said they would have granted the prison officials’ request for a stay of the Ninth Circuit’s ruling.

Ms. Edmo, who was convicted of sexually assaulting a sleeping 15-year-old boy, is scheduled to be released next year. She has been treated for gender dysphoria, the psychological distress caused by incongruence between experienced gender and that assigned at birth, with hormone therapy and counseling.

A prison psychiatrist, Dr. Scott Eliason, denied her request for surgery notwithstanding two attempts by Ms. Edmo at self-castration. Ms. Edmo sued, saying that the failure to provide the surgery violated the Eighth Amendment’s ban on cruel and unusual punishment.

She won in the trial court and before a unanimous three-judge panel of the Ninth Circuit. “It is no leap to conclude that Edmo’s severe, ongoing psychological distress and the high risk of self-castration and suicide she faces absent surgery constitute irreparable harm,” the panel wrote in an unsigned opinion.

After the full Ninth Circuit’s refusal to rehear the case, Judge Diarmuid O’Scannlain, joined by eight other judges, wrote that the panel had put too much weight on standards published by the World Professional Association for Transgender Health, which he called “a controversial self-described advocacy group that dresses up ideological commitments as evidence-based conclusions.”

“I do not know whether sex-reassignment surgery will ameliorate or exacerbate Adree Edmo’s suffering,” Judge O’Scannlain wrote. “Fortunately, the Constitution does not ask federal judges to put on white coats and decide vexed questions of psychiatric medicine.”

In urging the Supreme Court to intercede, prison officials wrote that “under the Ninth Circuit’s interpretation, medical decision-making that conflicts with the views of advocacy organizations is enough to establish an Eighth Amendment violation.”

Ms. Edmo’s lawyers responded that the association’s standards were widely accepted by medical groups, were said to provide “the best guidance” by lawyers for the prison officials in proceedings before the trial court and were at a minimum a useful starting point.

In any event, her brief said, the lower courts’ decisions established no universal standards and were closely tailored to her circumstances.

“The evidentiary record established that gender confirmation surgery is a safe and effective treatment for individuals with severe gender dysphoria and that this treatment was medically necessary for Ms. Edmo, who experiences such profound distress that she has attempted to castrate herself twice and now cuts her arms in an attempt to distract herself from her acute gender dysphoria,” the brief said. “Whether one person or 100 people have previously been provided gender confirmation surgery in prison is not relevant to determining whether that surgery is medically necessary for Ms. Edmo.”