The Serbian Orthodox Church had always ben part of the patriarchate of constantinople until its autocephaly was recognized by the Ecumenical patriarchate and the dioceses of Karlotsk and Beograd got united.
Some byzantine slavs from Macedonia, Serbia and Croatia became catholics in the XVII and the popes established a diocese in Krizevsci. The eastern rite catholics were primarily croatian and not ethnic serbian.
In 1947 the communists took the government in Yugoslavia and the pro-soviet factions tried to submiss the Serbian Church to Moscow. But when the moderate socialists headded by Josip Broz "Tito" won the political battle against the pro-russians, the new government tried to preserve the independence of the Serbian Church.
Tito was very concerned about the ethnical problems between serbs (orthodox) and the croatians (latin catholics)and thought that a religious union between these churches could sign (at least nominaly) a brotherhood between both ethnic groups.
At the time the romanian, soviet and czech regimes were supressing the eastern catholic churches and forcing to unite them with the orthodox, some yugoslavs tried to unite the Serbian Orthodox Church with Rome. In spite of this, the union never happened because of the opposition of the russian church and the croatian latin prelates.
Do you know something about the serbian catholic church in the USA?