“Don’t call us, we’ll call you” (entertainment saying)

“Don’t call us, we’ll call you” is an old brush-off line given to an actor after a failed audition. The call from the play’s producer never comes.
 
The origin of the phrase is unknown, but it’s cited by New York columnist Dorothy Kilgallen in a 1944 column.
 
 
(Oxford English Dictionary)
colloq. (orig. U.S.). don’t call us, we’ll call you and variants: further approaches would be unwelcome or futile; there is no need to pursue your application or enquiry any further. Also shortened as don’t call us.
Prob. introduced as a clichéd way of dismissing unsuccessful candidates at theatrical auditions (cf. quot. 1952).
1948 Lima (Ohio) News 3 Mar. 11/6 The Czechs now get a solid hour of the American viewpoint [on the radio]..that leaves 23 for Moscow monologs. They have been promised time of their own when something opens up. The way Stalin left it was ‘don’t call us ... we’ll call you’.
1952 East Liverpool (Ohio) Rev. 29 Oct. 12/2 Hollywood has a word—or two—for it… Everyone has heard the brushoff line: ‘Don’t call us. We’ll call you.’
1959 ‘B. WILDER’ & I. A. L. DIAMOND Some like it Hot (film script) 137 First Henchman. Room 413—we’ll be in touch. Jerry (coyly) Don’t call us—we’ll call you.
1971 Evening Standard 19 Aug. 3/4 The Labour Exchange never seems to have a job and the ones you do manage to go after almost always say ‘don’t call us, we’ll call you’.
1987 M. BOLTON Testing v. 70 Daintry said he’ll keep us informed… I think he meant don’t call us, we’ll call you.
1993 F. COOPER I believe in Angels (BNC) 80 I’d conjured up a rather camp Major Sager… I felt like a jaded casting director as I banished him to the wastepaper bin. Don’t call us, old chap.
2000 Calgary Sun (Electronic ed.) 22 Sept., Endorsement contracts hinge on where you finish. Gold is bonanza, silver pretty good, bronze not bad. Fourth place? Don’t call us, we’ll call you.
   
17 March 1944, Lowell (MA) Sun, Dorothy Kilgallen column, pg. 23, cols. 3-4:
Fables from the Forties:
Our heroine could have had any number of good jobs behind a desk, but her passion was singing. She’d have sung for nothing if any one had let her, but even at those rates the opportunities were few and far between. Audition after audition left her with nothing but “Sorry” and “Not the type” and “Don’t call us, we’ll call you” and a heart that was close to breaking.
 
3 March 1948, Lima (OH) News, “One Man’s Opinion” by Walter Kiernan, pg. 11, col. 6:
America broadcasts to Czecho-Slovakia but it doesn’t look as tho radio will ever replace the old fashioned fifth column. The Czechs now get a solid hour of the American viewpoint ... that leaves 23 for Moscow monologs. They have been promised time of their own when something opens up. The way Stalin left it was “don’t call us ... we’ll call you.”
 
27 January 1949, Brownsville (TX) Herald, “In Hollywood, International Star Brisson Has Interesting Life Story” by Erskine Johnson, pg. 12, col. 2:
Carl Brisson was one of the first movie stars I ever met. (...) He made the rounds of the studios. Yes, producers and directors remembered his big hit on the screen in 1934, but, well, “come around some other day but don’t call us, we’ll call you.”
 
29 October 1952, New York (NY) Herald Tribune, “Radio and Television” by John Crosby, pg. 25, col. 1:
“Well, Bully for You”
HOLLYWOOD.
I have in the past discoursed on the vagaries of the language used in advertising circles. Today, kiddies, the subject is Hollywood English, about which a whole lexicography could be issued. In fact, if you’re not reasonably hep, you could stay here for weeks and not understand a single word any one said.
(...)
Every one has heard the brushoff line: “Don’t call us. We’ll call you.” Out here, though, it’s “Call you tomorrow.”  Tomorrow never comes.
 
Google Books
The Blackboard Jungle:
A Novel
By Evan Hunter
New York, NY: Simon and Schuster
1954
Pg. 4:
... the gold cuff links glittering in the sunlight when his jacket sleeve pulled back — and then leaned forward smiling. “Don’t call us, we’ll call you.”
     
Google Books
I Love Her, That’s Why!:
An Autobiography
By George Burns
New York, NY: Simon and Schuster
1955
Pg. 159:
Instead of going home with a baby, she was told to go home and they would call her in a few months: “Don’t call us; we’ll call you.”
 
16 June 1963, New York (NY) Herald Tribune, magazine, pg. 4:
“Don’t call us, we’ll call you…”
But the young actor can’t sit and wait for the big break—he must go out and seek it, however wearying the hunt.