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According to https://www.wilsoncenter.org/publication/new-evidence-romania-and-the-warsaw-pact-1955-1989#sthash.fQcgY9zu.dpuf
"He [Emil Bodnaras, Romanian Minister of Transport and Communications, a key figure in the Romanian Party's support for Soviet intervention in Hungary] was probably instrumental in making arrangements for the detention of Imre Nagy in Romania for on 21 November he and Dej paid a visit to Janos Kadar, the new First Secretary of the Hungarian Communist Party, and on the following day Nagy was abducted by KGB officers and flown to Bucharest where he was granted what the Romanian Foreign Minister Grigore Preoteasa termed 'asylum'. In fact, he was held, along with other members of his government, in a safe house in a locality just north of Bucharest, where their interrogation was coordinated by Boris Shumilin, chief KGB adviser 'for counter-revolutionary affairs', and not allowed the visits from UN officials promised by Preoteasa to prove that he was not under duress. Shumilin permitted a senior RCP member, Valter Roman, who had fought in the International Brigade in Spain and was believed to be an NKVD officer, to question Nagy's associates. Many other prominent supporters of Nagy were interrogated in Romania, among them the Marxist critic Georgy Lukacs."
The source implies that Romania agreed for Nagy to be flown there in order to please the Soviets for future gains:
"Romania was the Soviet Union's most obedient ally during the Hungarian crisis. Its support of the Soviet Union went beyond the political arena into the domain of practical assistance and open encouragement... Additional bases were provided on Romanian soil to the Soviet forces, roads were widened, and railway traffic interrupted to carry military transport. Soviet satisfaction with Romania's role during October and November 1956 stood to the country's advantage two years later when Khrushchev decided to withdraw Soviet troops."
Edit: Detailed explanation given in this book The First Domino: International Decision Making During the Hungarian Crisis from page 131 onwards.
"While Prime Minister, Imre Nagy had instituted a number of measures to improve Hungarian-Romanian relations. For some reason he trusted Gheorghiu-Dej [general secretary of the Romanian Communist Party]."
However, as established above, Romania desired to please the Russians and betrayed him. This source continues to give a detailed account of what happened and further explanation of Romania's involvement.