Not only was manipulated, but I can tell you more: after the referendum, a coup d'etat took place...
But I guess it's better to return at the beginning ot the story.
Between 1922 and 1943 Italy was ruled by the fascist government of Benito Mussolini, and King Vittorio Emanuele III didn't oppose to this totalitarianism.
In 1940 Mussolini led Italy in the Second World War: he was the only person in Italy who wanted that, and the italian army was not able to share in a war: there weren't equipments, and a lot of young soldiers were sent to fight even if they didn't had had any kind of weapon in their hands before.
So, since the beginning of the war everything went wrong for the italian army, and for Italy; Italy fought for the first three years of war only thanks to the helps from the german army.
People was deeply unhappy, and in 1943 also the fascist main body started to understand that; so, on 25 July 1943 the Grand Council of Fascism deposed Mussolini, who was arrested.
In september the armistice between Italy and Allied armed forces was signed, and the Nazis invaded the north Italy, where partisans fought against the occupying german forces. The south of Italy was ruled by the legal government of Badoglio and later of Bonomi.
Between 1943 and 1945 the partisans (who mostly were supported and led by the main antifascist political powers, communists, socialists, christian-democratics and liberals) fought to free the north Italy, and these parties, that joined the National Liberation Committee, started to rule the the north of the Country.
The parties of the NLC were mostly anti-monarchist; and people put the responsability for all happened on the King, who didn't oppose to fascism, and so he was thought responsable for the fact that at the end of the war Italy was a severely damaged country, with a lot of victims, a destroyed economy, and a desperate general condition.
After the complete liberation of Italy, and the end of the war, the north Italy was mostly against the Monarchy, while the south was faithful to the King.
Something had to change, and maybe if the King would have abdicated in 1944 or 1945 would have been better.
Because of this strong internal opposition to the Monarchy, the King signed a decree prescribing the referendum to choose the form for the state, that took place on 2 June 1946.
The political campaign was framed by incidents, mostly in the north Italy, where monarchists were fought by both republicans and fascists; some politicians uses also personal attacks against the old King and the new King Umberto II, who became King after the (tardy) abdication of his Father, on 9 may 1946, less that a month before the referendum; King Umberto, for example, was accused to be homosexual, and in a deeply catholic country this was a heavy accuse (even if false).
The referendum took place, and was won by the republicans: 12 millions votes vs 10 millions for the Monarchy.
The Supreme Court of Cassation had to proclaim the Republic on 12 June, but on this date only the results of the referendum were read; no proclamation, that was postponed to the 18 June.
We have to remember that the Court of Cassation was the only body with the power of proclaim the winner of the referendum.
On that night, the Prime Minister De Gasperi proclaimed the republic, illegally.
The following day te King decided to leave: if he had opponed to the proclamation of the government, a new civil war would have begun. And he didn't want this: that's the reason of his leaving.
About the manipulation of the referendum, we have to notice some things:
1-Many prisoners of war were in prison and not able to vote;
2-Some provinces (Trieste, Bolzano) had not yet been reintegrated into Italy, and so had not been included in the vote;
3-The number of voters recorded was higher than the number of the electors (at least it seems to be so);
4-De Gasperi had no powers to proclaim the Republic.
