Voters across the country queued early in the morning for a ballot that many regard as crucial to their future - even though most have never seen the text.
It provides for a decentralised political system with provincial administrations responsible for local decision-making and controlling 40% of public funds. It also limits the president to two five-year terms, and requires the president to nominate a prime minister from the parliamentary majority.
Voting in many places began an hour or two late and there were isolated clashes in some places.
Riot police in Kinshasa, the capital, clashed with a group of about 20 youths who gathered outside a polling station and told people not to vote. The youths began hurling stones at the police, who detained at least one of them.
Fears of violence
Patrice Bovile, an accredited election observer, said: "The level of participation here is very low. When people registered here this place was packed. Maybe it is because of the calls for a boycott and fears of violence."
In Goma, police beat a couple of dozen people with batons as they tried to force a crowd of nearly 200 into a single queue at a polling station, according to a Reuters reporter.
There was also fighting involving Kinyarwanda speakers, regarded by some as having sided with Rwandan forces during a complex five-year war that dragged in six foreign armies.
Jacqueline Chernard, a UK spokeswoman, said: "There was serious fighting between some Congolese voters and Congolese Rwandaphones who were being accused by their colleagues of being Rwandans and having no legitimacy in today's vote."
The referendum is the first step towards polls planned for next year and are meant to draw a line under Congo's last conflict, which officially ended in 2003.
Congo was renamed Zaire during the 32-year dictatorship of Mobutu Sese Seko. The country became a byword for corruption under Mobutu and its infrastructure decayed as state resources were stolen.
Mobutu was removed in 1997 by Laurent Kabila, whose son, Joseph, is now president.
About 25 million people registered to vote in the referendum and the subsequent local, parliamentary and presidential elections, which under a peace deal must be held by next June.
Successful elections are seen as the key to consolidating peace in the mineral-rich country, the size of Western Europe, but now lacking in the most basic infrastructure.
Thousands of gunmen still roam the hills of the east, terrorising civilians.
The UN, which has its biggest peacekeeping force in the country, says Congo's polls are the most complex and difficult it has ever been involved in.