I think they are so rare there is not a standard procedure.

Ethel and Julius Rosenberg executed by electric chair for conspiring to pass US atomic secrets in 1953: Following Clip from History.com It didn't say if it was public or not, but at SIng Sing Prison.

On June 19, 1953, Julius and Ethel Rosenberg, who were convicted of conspiring to pass U.S. atomic secrets to the Soviets, are executed at Sing Sing Prison in Ossining, New York. Both refused to admit any wrongdoing and proclaimed their innocence right up to the time of their deaths, by the electric chair. The Rosenbergs were the first U.S. citizens to be convicted and executed for espionage during peacetime and their case remains controversial to this day.

Julius Rosenberg was an engineer for the U.S. Army Signal Corps who was born in New York on May 12, 1918. His wife, born Ethel Greenglass, also in New York, on September 28, 1915, worked as a secretary. The couple met as members of the Young Communist League, married in 1939 and had two sons.

Julius Rosenberg was arrested on suspicion of espionage on June 17, 1950, and accused of heading a spy ring that passed top-secret information concerning the atomic bomb to the Soviet Union. Ethel was arrested two months later. The Rosenbergs were implicated by David Greenglass, Ethel’s younger brother and a former army sergeant and machinist at Los Alamos, the secret atomic bomb lab in New Mexico. Greenglass, who himself had confessed to providing nuclear secrets to the Soviets through an intermediary, testified against his sister and brother-in-law in court. He later served 10 years in prison.

The Rosenbergs vigorously protested their innocence, but after a brief trial that began on March 6, 1951, and attracted much media attention, the couple was convicted. On April 5, 1951, a judge sentenced them to death and the pair was taken to Sing Sing to await execution.

During the next two years, the couple became the subject of both national and international debate. Some people believed that the Rosenbergs were the victims of a surge of hysterical anti-communist feeling in the United States, and protested that the death sentence handed down was cruel and unusual punishment. Many Americans, however, believed that the Rosenbergs had been dealt with justly. They agreed with President Dwight D. Eisenhower when he issued a statement declining to invoke executive clemency for the pair. He stated, “I can only say that, by immeasurably increasing the chances of atomic war, the Rosenbergs may have condemned to death tens of millions of innocent people all over the world. The execution of two human beings is a grave matter. But even graver is the thought of the millions of dead whose deaths may be directly attributable to what these spies have done.”