If the court agrees to consider the motion, it can automatically suspend plans for the referendum, which Basque authorities want to hold on October 25.
The referendum would put two questions to a vote. The first asks Basques if they favour a negotiated solution to the separatist conflict if armed group Eta is willing to end violence.
The second asks if they agree that all Basque political parties should work toward an agreement on what it calls Basques' right to decide their future and that this should be put to a second referendum before the end of 2010.
When Basques talk about such self-determination, critics elsewhere in the country see this as advocating a breakaway from Spain.
The Basque regional government, run by a coalition of three moderate nationalist parties that lack a majority, received help on Friday from a pro-independence party that supports ETA.
The Communist party of the Basque Lands allowed one of its nine lawmakers to vote in favour of the referendum.
The final tally in the 75-seat Basque legislature was 34-33 with seven abstentions. One legislator was absent.
Jose Luis Rodriguez Zapatero, the Spanish prime minister, says the planned referendum is unconstitutional because only Spain's government, not a regional administration, can authorise such a vote.
Juan Jose Ibarretxe, the Basque regional president first raised the idea of the referendum late last year as part of a "road map'' peace plan following the collapse of negotiations between the Spanish government and Eta.
In a debate before Friday's vote, Ibarretxe denied the vote was divisive, and insisted there is nothing wrong with simply asking people what they want.
"Democracy is not about keeping society from having an opinion and expressing it, but rather about consulting, hearing citizens' desires and respecting them,'' he said.
Ibarretxe is also being criticised for breaking on a pledge to hold a referendum only if Eta, which has killed around 825 people since 1968, puts an end to attacks.
The group, which wants an independent homeland for Basques in parts of northern Spain and southwestern France, has staged more than 20 attacks since ending a ceasefire in December 2006 with a car bombing at a Madrid airport parking garage that killed two people.
Eta has since then been blamed for the killings of two Spanish police officers in southern France in December 2007, a local Basque politician in March , and another police officer in May.