“We are now seeking early talks with the European Commission to discuss the specific process of Scotland becoming independent,” she added.

Without a precedent there may be no legal certainty, but Mr. Barroso’s statement is causing problems for Ms. Sturgeon’s Scottish National Party, which campaigns for independence, because it contradicts its position that an autonomous Scotland would negotiate its new terms of membership from inside the European Union.

While Britain has a cast-iron, legally binding, opt-out from membership of the European single currency, that would not necessarily transfer automatically were a new application for membership made. Nor would Scotland necessarily inherit Britain’s opt-out from Europe’s passport free travel area, the Schengen zone.

“In Scotland it’s not so much the threat of being excluded as the threat that you might be dragged further into European integration than you wanted,” said John Curtice, professor of politics at the University of Strathclyde.

With the rest of Britain remaining outside the Schengen area, membership would make little sense for Scotland, raising the possibility of controls at the frontier with England. Mr. Curtice said that the idea of euro membership was probably no more popular in Scotland than in the rest of euroskeptic Britain.

Meanwhile the intervention of Mr. Barroso threatens to undermine the credibility of the S.N.P. by contradicting one of its arguments. “I think it raises doubt in people’s minds about whether the S.N.P. has fully grasped the issue, and adds an element of uncertainty which might persuade people to hold on to nurse for fear of something worse,” Mr. Curtice said.

In another complication, any application for membership would need to be approved by all E.U. nations. That means that, even if a divorce was agreed with the rest of Britain, Scotland’s negotiations might be obstructed by other nations, like Spain, for fear of setting a precedent.