The vote on Sunday had been banned by a constitutional court, which also ruled the holiday on January 9th discriminates against Bosnia's Catholic Croats and Muslim Bosniaks.
The date commemorates the day in 1992 when Bosnia Serbs declared the establishment of their own state, Republika Srpska, which ignited a devastating war between 1992 and 1995.
The conflict, which left 100,000 people dead and displaced half the nation's population, saw Muslim Bosniaks and Catholic Croats persecuted and almost entirely forced out.
Republika Srpska did not gain independence after the war, but instead became an autonomous area of Bosnia.
Goran Salihovic, the top prosecutor in Bosnia, said the case would be treated as a "priority", adding particular individuals will be summoned for questioning.
According to referendum organisers, 99.81 per cent of voters in Republika Srpska backed the holiday and turnout was 55.7 per cent.
The Bosnian Serb leader, Milorad Dodik, who organised the referendum, celebrated the result on Sunday in Republika Srpska's wartime capital, Pale, joined by thousands of people and Serb flags.
He said: "I'm so proud ...of all those who voted today, and I have to say - shame on all Serbs who did not show up at the referendum today."
Backed by Russia, the referendum was opposed by Western officials who threatened imposing travel bans on its leaders and freezing their assets.
While opposition parties claim the referendum was a bid to divert attention away from issues such as corruption ahead of local elections, authorities say they do plan to change the law so those who do not want to celebrate the holiday can abstain.
Nevertheless, responsibility for Sunday's unconstitutional referendum could bring a prison sentence of between six months and five years.