I found some interesting information... according to the American Film Institute:
[Show spoiler]
On 19 Feb 1960, the PCA viewed the completed film, which it refused to approve. According to an internal memo, the film was rejected because of the beginning scene between Sam and Marion, which was “entirely too passionate”; a sexually suggestive line uttered by “Tom Cassidy”; and the shower murder sequence. The memo stated that the sequence had “a number of shots, some impressionistic, some completely realistic, of the girl’s nude body. All of these shots are in violation of the Code, which prohibits nudity ‘in fact or in silhouette.’” It was further declared that Norman watching Marion undress was too sexually suggestive and had to be cut so that he would only see her in her bra and slip rather than explicitly taking off her bra. On 3 Mar 1960, the office issued Paramount a seal of approval “based upon the revised scenes as reviewed in our projection room” the previous day, so presumably the cuts demanded by the PCA were made.
The Hitchcock papers reveal that the National Catholic Legion of Decency demanded three cuts before giving the picture a “B,” or “morally objectionable in part for all” rating. The Legion required that scenes of Marion removing her bra be deleted, that the shots showing Norman washing his hands of blood be shortened and that the number of times Arbogast is stabbed be reduced from four to two. Psycho was eventually issued the “B” rating by the Legion, which announced: “The sensational use of sex and the excessive violence, which partially mar the development of the story, are considered to be entirely lacking in dramatic justification and to be highly objectionable.”
Information in the Hitchcock Collection suggests that there was a “foreign version” of the picture, in which the opening sequence between Sam and Marion contained footage excised from the American release. A 21 Jun 1960 entry in HR 's "Rambling Reporter" column asserted that the European version would contain more nudity in the shower sequence. A Feb 1961 NYT story about Geoffrey I. Shurlock, the head of the PCA, reported that although Shurlock had been criticized for allowing the frank sequence, “it is known that this scene was much more torrid as filmed originally; Shurlock forced Hitchcock to reshoot the entire sequence to make it less sexy.” Modern sources allege, however, that Hitchcock offered to redo the sequence, but only if someone from the PCA office was present at the time to approve it, and when no PCA officials attended the scheduled reshoot, the matter was not pursued.
Elsewhere, on their details page, they have the information that there were two pick-up days of shooting, one on Feb 15th and one on March 1st. To me, the latter date seems to suggest that the opening was reshot to get approval from the PCA, and that the "Hitchcock tricked his way out of it" story is apocryphal, but I'm not going to say I'm sure about that.
So it seems like the "European" cut was made after the PCA / Hays people made some cuts, but before the three specific cuts which were made for the National Catholic Legion of Decency. If the Legion had given the film a "C", millions of members would have (theoretically) boycotted the film, so cuts were made to get the lighter B rating.
As much as I hate to agree with Bates Motel, that seems like pretty good specific evidence that the cuts pre-date the initial US theatrical release.
https://catalog.afi.com/Catalog/moviedetails/53260
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