I found these comments on "Star Dust" by a user named Bernhard on the sinatrafamily.com bulletin board (link):
"The record [Victor 27233] entered the Billboard Charts on December 27, 1940 (reached #7).
Sinatra and Dorsey recorded the song (which has music by Hoagy Carmichael, and words by Mitchell Parish, and was first published in 1927) on November 11, 1940. Since they were appearing in concert there at the time, this studio session took place at the Hollywood Palladium Theatre (6215 Sunset Blvd). The arrangement ... was supplied by Sy Oliver (with whom FS would later in 1961 record the "I Remember Tommy" album on Reprise).
The orchestra personnel for the 11-11-40 recording as featured on that single is as follows:
Chuck Peterson, Ray Linn, Ziggy Elman (trumpet); Tommy Dorsey, George Arus, Les Jenkins, Lowell Martin (trombone); Fred Stulce, Heinie Beau (alto sax); Don Lodice, Paul Mason (tenor sax); Johnny Mince (clarinet & alto sax); Clark Yocum (guitar); Sid Weiss (bass); Joe Bushkin (piano); Buddy Rich (drums); Frank Sinatra (vocal); The Pied Pipers: Jo Stafford, Clark Yocum, Chuck Lowry, John Huddleston (vocal)."
An anonymous Guest added:
"While that is the complete personnel for the session—during which another song ("Not So Long Ago") was also recorded—not all of these played on "Star Dust." An actual listening reveals there is no brass, other than a Tommy Dorsey trombone solo interlude, and probably not the full complement of saxophones. Most of the song consists of Frank Sinatra's vocal, accompanied by a piano-guitar-bass-drums rhythm section and the Pied Pipers. Joe Bushkin plays celeste in the intro and ending. Jo Stafford does a wonderful short solo vocal ("Ah, but that was long ago, and now my consolation is in the stardust of a song.")"
@SeberHusky
Here's another incorrect release date added by you via the Add Missing Info and the Make Correction tools respectively. As already said in the Record Notes, the B-side was recorded on October 16, 1940 and the A-side was recorded on November 11, 1940. Thus the release date of "11 Nov 1940" can by no means be right. At best, deduced from the recording dates on http://www.78discography.com/vic27000.html, we can guess that Victor 27233 was probably released in December 1940.