According to author Stephen Rebello, in his extremely interesting and well-researched book, Alfred Hitchcock and the Making of Psycho (St. Martin's Griffin, 1998, p. 138), on January 8, 1960, director Alfred Hitchcock sent a memo to his sound men, Waldon O. Watson and William Russell, giving them explicit instructions about the role of sound in the shower scene. Surprisingly, no mention is made of music. We can safely assume, I think, that the (now famous) shower scene of Psycho was being edited--though was certainly not completed--on Monday, January 11, 1960. The premiere of the film was slightly over five months away.
The title of Rebello's book about the film is carefully worded, because it is clear that Alfred Hitchock cannot take full credit for the success of Psycho--indeed, his role in post-production was virtually non-existent. Revealingly, after screening a rough cut of the film, Hitchcock himself thought the film was terrible, and considered cutting it down and salvaging it by showing it as an episode of Alfred Hitchcock Presents. The achievement of Psycho, such as it is, seems in retrospect to have been the result of two factors: the extremely talented artists with which Hitchcock surrounded himself--first and foremost, film editor George Tomasini, the aforementioned sound designers, Waldon O. Watson and William Russell, and composer Bernard Herrmann--and the first generation of American critics (e. g., Andrew Sarris) who had adopted the assumptions and perspectives of the auteur theory. The achievement of the film itself is largely a technical one; its status as a "classic" is largely a discursive one, Hitchcock having pride of place as the first movie director bestowed the imprimatur of auteur. What was Romanticism in the nineteenth century was called Modernism in the twentieth, and like all Modernists, Hitchcock took to heart the principle of the self as art, and ran with it. (I highly recommend Robert E. Kapsis's book, Hitchcock: The Making of a Reputation, University of Chicago Press, 1990.)
The French New Wave critics who had disseminated and promoted the auteur theory through the journal Cahiers du Cinema—Francois Truffaut, Eric Rohmer, Claude Chabrol and Jean-Luc Godard—had one primary champion, and that was Alfred Hitchcock. Eric Rohmer and Claude Chabrol's Hitchcock was published in 1957, shortly after the release of Hitchcock’s The Wrong Man (1956), and was an early important work of auteur theory (although it remained untranslated into English for many years). The reason for Rohmer's and Chabrol's choice to champion Hitchcock most certainly was because they perceived him to be much like themselves: Catholic, politically liberal, intelligent, and Modern. However, since auteurists (at least the French ones) always had trouble with what they called a "Tradition of Quality," the auteurist position tended to champion directors who sometimes made bad films (e. g., besides Hitchcock, Otto Preminger) or were not very nice (e. g., Sam Peckinpah) or were not very intelligent (e.g., name omitted). And as one might expect, the hallowed pantheon of auteurs was also always a boy's club--the offices of Cahiers du Cinema had pin-ups on the walls well into the 1960s.
My friend Frank Mazzola, who grew up in Hollywood and eventually became a respected film editor, told me that while he was an apprentice editor in the late 1950s and early 1960s, he was a "gofer" at Universal while George Tomasini was editing Psycho and Bob Lawrence was editing Spartacus (the films were released about three months apart in 1960). Tomasini's offices were at one end of the floor and Lawrence's were at the other. Saul Bass, who created the title sequences for both films, was also there, moving between both sets of offices. While Frank saw Kubrick, he never saw Hitchcock, although Hitchcock had a office/bungalow at Universal. The famous shower sequence in Psycho was created not by Hitchcock but by Tomasini, sound designers Watson and Russell, by Bernard Herrmann's strings--and, according to Stephen Rebello, by Mrs. Hitchcock, who in her screening of the sequence was the only one of them all to notice that although she's presumably dead when she falls to the floor, Janet Leigh blinked, forcing Tomasini to insert a brief cutaway to the shower head.
I should note that Tomasini was Hitchcock's editor of choice for a decade, from Rear Window (1954) through Marnie (1964). After Tomasini's early death in November 1964 at age 55, Hitchcock made only four more films in a period of twelve years, none of which are very interesting. For whatever reason, it would seem that Hitchcock lost interest in making movies after Tomasini's death.
In retrospect, the major contribution of the French auteur theorists is that they invented film studies (and directors such as Alfred Hitchcock as well), for without the notion of the director as writer, film courses never would have been able to be offered in university English departments, which is where film studies courses were first offered. Of course, there are other reasons that contributed to rise of film studies--the collapse of university enrollments following the abolition of the draft in the early 1970s being one, but nonetheless the auteur theory was an extremely important factor in the development of film studies in the late 1960s and 1970s.
Has the significance of the shower sequence been over-emphasized in critical discussions of Psycho? For interesting discussion of that question, go here. For an excerpt from Rebello's book, as well as contemporary film reviews in addition to critical interpretations and re-assessments of Psycho, see Robert Kolker, Ed., Alfred Hitchcock's Psycho: A Casebook, Oxford University Press, 2004).