NEW YORK — The producers of “Big River” have received word from CBS that their show will not be allowed to perform on the telecast from Radio City Music Hall despite having been nominated for musical revival.

A rep for the Tonys confirmed: “CBS has mandated that only shows that are currently running will perform.” He said the decision had been made due to the telecast’s “time constraints.”

There is recent precedent for such an omission: Last season, “Amour” closed in November, received a nom for new musical the following May, but did not perform on the Tony show in June.

“We’re incredibly sad and disappointed that CBS won’t let us perform on the Tonys,” said Jeff Calhoun, who directed the Deaf-West production of “Big River,” which was produced on Broadway in association with Roundabout.

When the 1985 Roger Miller/William Hauptman tuner returned to Broadway last summer, critics called the new production groundbreaking in its innovative use of American Sign Language and the double-casting of speaking and nonspeaking actors.

According to Calhoun, Tony producers supported including a number from “Big River” in the telecast, but CBS nixed the idea.

The network could argue that shuttered shows don’t have adequate rehearsal time, not to mention the requisite sets and costumes, to stage a TV-worthy production number.

“That is not the case with ‘Big River,’ ” Calhoun challenged.

Road rehearsal

The show has been in rehearsal in recent weeks for its national tour, which kicks off June 11 at the Curran Theater in San Francisco. Not only does “Big River” have the necessary sets and costumes, three headliners from the 2003 Broadway production are back onboard for the tour: Daniel H. Jenkins, Tyrone Giordano and Michael McElroy, who is nommed this year for featured actor in a musical. They had planned to perform the song “Muddy River” on the telecast.

In a major time-constraint snafu, the 1999 Tony telecast skedded a song from the still-running and nominated “It Ain’t Nothin’ but the Blues” and then pulled the number at the last minute as the clock ran out.

If CBS doesn’t reverse its decision on “Big River,” the show may be reduced to a short B-roll segment on the telecast, which is how “Amour” was honored last year.

The new shuttered-shows-can’t-perform practice runs in the face of some great Tony moments from the past. In 1979, Dorothy Loudon got passed over for the leading actress award, but she stole the telecast singing a solo number, “Fifty Percent,” from “Ballroom.” The musical had been closed for months.