Psycho's Antecedents [spoilers ahead]

1a. Dead of Night (1945)
Dead of Night (1945) is a brilliant horror anthology movie whose tone (macabre but humorous) and specifics anticipate both Alfred Hitchcock Presents and Rod Serling's The Twilight Zone. The film's final, monstrous, circular dream-within-a-dream twist is so brilliant conceived and worked that it's directly inspired several episodes of current Netflix 'it"-show, Black Mirror (especially the Jon Hamm-starring movie-length episode, 'White Christmas').

Setting aside the final twist segment involving the framing narrative that's undoubtedly DON's crowning achievement, the most distinguished and famous individual segment within DON is 'The Ventriloquist's Dummy' starring Michael Redgrave and directed by Alberto Cavalcanti. (This segment was restaged as a Twilight Zone ep. 'The Dummy' starring Cliff Robertson.) The connection of this tale with Psycho is made immediately afterwards in a Psychologist's debrief back in the framing story. Here's that dialogue:

Dr Van Sratten: One of the most complete examples of dual identity in the history of medical science.
Someone else: You mean that half the time Frere was Frere and the other half he was his dummy?
Dr Van Sratten: Exactly. And in the end, the dummy got the upper hand entirely.
Someone else: But how did the dummy get from one room to another? Under its own steam?
Dr Van Sratten: Without knowing what he was doing, Frere took it himself. Impelled by the dominating Hugo half of his mind. That is the scientific explanation. But, no doubt, you people would prefer a more colourful one. That Hugo had become endowed with an existence of his own.

DON's "the dummy got the upper hand entirely" is very like Psycho (1960)'s "in Norman's case, the dominant personality has won".

Note that the Ventriloquist story, which ends right before the Psychologist debrief, ends with the Ventriloquist (Redgrave) in a largely white cell speaking with his own mouth in the dummy's voice. This is essentially the same image with the same import as Norman in a lonely white cell with Mother's voice over the image of Norman's face. The paradox of the ventriloquized ventriloquist (the ventriloquist who's become his dummy's dummy) is essentially the same as the paradox of the matricidal son who's been overtaken and betrayed by his mother. It helps that, especially in 1945, Redgrave had the slightly stiff but boyish look that Perkins, Lawrence Harvey, Michael Rennie, and a bunch of others all had (acting perhaps as anti-Mitchums, anti-Lancasters, anti-Waynes) in the '50s and '60s. Or put the other way around (at ecarle's suggestion): had Psycho been made by Hitchcock in England in the '40s, Redgrave would have been his Norman Bate (except Psycho wouldn't have been made in England or anywhere else in the '40s).

Ecarle has usefully observed the following parallels earlier in the story:
1. The dummy tells ANOTHER ventriloquist that he wants to "ditch" Redgrave because he feels that Redgrave is a loser and the dummy wants to "trade up" to a better partner. The dummy relentlessly berates Redgrave as a loser type -- and that's Mother's yelling at Norman, isn't it?("I'm sorry, boy, but you do manage to look ludicrous when you try to give me orders" or "Or do I have to, because you haven't got the guts?") Of course, in both cases, the "live" person is having the fake person tear himself down. (The sadist and the masochist in the same body.)
2. Near the story's end, Redgrave tries to blame the dummy for almost killing the other ventriloquist, but the dummy's having none of it: "Not so fast, buster -- don't try to pin this on ME!"(or something funny like that.) This matches how at the end of Psycho, Mother is switching back the evil on Norman: "Its hard for a mother to condemn her own son, but he was always BAD. He tried to tell them that I killed those girls, and that man. He'll be locked away now.")
3. Hugo the Dummy insults the TWO ladies out with a guy who turns out to be more of a bruiser than he looks. He offers Redgrave the chance to apologize for his dummy's insults to the ladies, then punches Redgrave out when the latter is too drunk(or spellbound in madness) to respond. That the dummy proves a "nasty character" compared to the harmless, ineffectual Redgrave foreshadows Psycho's ferocious mother lurking behind essentially sweet Norman.

1b. Dead of Night (1945)
There are two main pathways for DON to have influenced Psycho (i) though Hitch himself and (ii) through Robert Bloch,the author of the novella, Psycho on which the film was based.

The argument for the second pathway is straightforward. Here is how Bloch has Sam Loomis recount Dr Steiner's diagnosis of Norman to Lila:

"It isn't quite that simple. According to Steiner, Bates was now a multiple personality with at least three facets. There was _Norman_, the little boy who needed his mother and hated anything or anyone who came between him and her. Then, _Norma_, the mother, who could not be allowed to die. The third aspect might be called _Normal_--the adult Norman Bates, who had to go through the daily routine of living, and conceal the existence of the other personalities from the world. Of course, the three weren't entirely distinct entities, and each contained elements of the other. Dr. Steiner called it an 'unholy trinity.'
"But the adult Norman Bates kept control well enough so that he was discharged from the hospital. He went back to run the motel, and it was then that he felt the strain. What weighed on him most, as an adult personality, was the guilty knowledge of his mother's death. Preserving her room was not enough. He wanted to preserve her, too; preserve her physically, so that the illusion of her living presence would suppress the guilt feelings.
"So he brought her back, actually brought her back from the grave and gave her a new life. He put her to bed at night, dressed her and took her down into the house by day. Naturally, he concealed all this from outsiders and he did it well. Arbogast must have seen the figure placed in the upstairs window, but there's no proof that anyone else did, in all those years."
"Then the horror wasn't in the house," Lila murmured. "It was in his head."
"Steiner says the relationship was like that of a ventriloquist and his dummy. Mother and _little_ Norman must have carried on regular conversations. And the adult Norman Bates probably rationalized the situation. He was able to pretend sanity, but who knows how much he really knew?

And the scenes in the novella between Norman and Mother are more extensive than in the movie, and her first belittling him and then at the end distancing herself from him (1 and 2 above) is even more pronounced. Thus the parallels between Bloch's Psycho and DON's Ventriloquist Dummy tale feel extensive.

The argument for the first pathway, for Hitch having seen and been impressed by DON, is more circumstantial. First, DON is from Ealing Studios which was run by Michael Balcon who'd given Hitchcock his start as a director at Gainsborough Pictures in the '20s, and produced for Hitchcock in the '30s, esp. The 39 Steps. We know for sure that Hitch kept a pretty close eye on Ealing's output probably in part because of that personal connection with Balcon, but consider too that Hitchcock loved Ealing's greatest film Kind Hearts and Coronets (1949) enough to restage it in 1957 for The Salt Lake Times! This link contains a sub-link to the whole Salt Lake Times photo-article. That photo-article contains the famous shots of Hitch dressed as a woman (catnip to Cultural Studies programs everywhere!), since in the article he plays versions of all eight roles that Alec Guinness played in KH&C, i.e., including suffragette Aunt Agatha.
Second, one of the writers on DON was Angus MacPhail. Immediately before DON, Macphail wrote the screenplays for two wartime propaganda shorts that Hitch directed, Bon Voyage and Aventure malgache, and immediately after DON, MacPhail did some writing for Hitchcock on Spellbound. Later MacPhail would have a hand in the Man Who Knew Too Much (1956) screenplay, and he'd co-write The Wrong Man (1956) with Maxwell Anderson. It's hard to believe that DON wouldn't have come up on one of those occasions. (Note that MacPhail also seems to have originated the term for and concept of the MacGuffin.)
Third, the star of the Ventriloquist Dummy segment, Michael Redgrave, had had a major role for Hitch in The Lady Vanishes (he's the musicologist, Gilbert).
To summarize: really, how likely is it that Hitch, a guy who in the early '40s was already a publisher of mystery anthologies in the UK, wouldn't check out the acclaimed first mystery-horror anthology picture made not just by his friends but also by his own personal 'if I hadn't gone to Hollywood', 'road-not-taken' studio? Not very, I'd say. (I'd guess that some Library or Archive in LA probably has definitive proof of Hitch catching DON and other Ealing Studios films in 1945 and 1946, but until then our circumstantial will have to do. )

1c. Dead Of Night (1945)
In my view, then, there's every reason to believe that Dead Of Night's DNA found its way into Psycho (1960)'s DNA probably via both Bloch and Hitch.

A final thought. Everyone knows that part of Psycho's importance is that it brought together Hitch's star-driven film side and his more disreputable, lucrative, teen-courting TV side. Keeping DON in mind as influence on Psycho deepens that basic perception by reminding us that Hitch's decision to come to Hollywood in 1939 had its price. It forced Hitchcock towards more elevated materials suitable for big stars like Ingrid Bergman, Gregory Peck, and Cary Grant, and away from his roots in exciting thrillers and mystery-publishing. Ealing Studios meanwhile would take up this banner. Hitchcock would get back to his UK roots in disreputable genres first with his TV shows, and then finally, triumphantly would merge all his horizons with Psycho.