The Spanish authorities have accused Mr. Puigdemont of rebellion and misuse of public funds, and a German regional court will decide within 60 days whether to send him back to face trial. But if the court chooses to extradite him only for the corruption charge, that would create a political and legal bind for the Spanish government, which would be barred from trying him for rebellion, the charge at the heart of the matter.
“Spain is creating a situation where Europe’s judges rather than its politicians are being asked to solve Catalonia,” said Sergi Pardos-Prado, a professor of politics at Oxford University. “At a time when the European Union needs more legitimacy and to reconnect with its citizens, how can this not make it seem like a distant and technocratic project?”
On Monday, Gonzalo Boye, a lawyer who represents two of the politicians wanted by Spain, told the Spanish news media that he was confident a foreign judge would not allow his clients to stand trial for rebellion. He even asked whether “Judge Llarena isn’t our best friend, because things are being handled in the worst possible manner.”
Mr. Puigdemont’s arrest has thrust Catalonia back onto the European agenda, potentially testing relations between Germany and Spain, after European governments had mostly managed to ignore the separatists’ political aspirations. The case also raises questions about whether Europe has a unified conception of the rule of law, and how it will respond to other secessionist movements.
Madrid is also seeking the arrest of other Catalan separatists who are in Scotland, Belgium and Switzerland, where officials have so far questioned whether their legal systems require the separatists’ extradition based on the rebellion charges brought by Spain. Mr. Puigdemont himself had been based in Belgium, where the European Union is headquartered, since late October. While Belgium never considered him a flight risk, a German judge has ordered that he should be provisionally kept in prison for that very reason.
The arrest comes at a particularly combustible time for the European Union, which is coping with Britain’s pending exit from the bloc, a right-wing populist upheaval in Italy, growing labor unrest in France, frictions between Brussels and the increasingly authoritarian governments of Hungary and Poland, and a growing clash with Russia.
It is also a difficult time for the Catalan separatists, who appear to be running out of options within the country’s political framework. After a botched declaration of independence in October, and new regional elections, the three separatist parties have been unable to resolve disputes among them and elect a new Catalan president.
Mr. Puigdemont and other separatists claim that Spain cannot give them a fair trial. That accusation is dismissed in Madrid as yet another affront by politicians who have repeatedly flouted court rulings in their drive toward independence.
“We can debate the specific approach of the prosecution and the judges, but there are strong legal grounds for this case,” said Enrique Gimbernat, professor of criminal law at Complutense University in Madrid.
Still, several Spanish legal experts acknowledge that state prosecutors are pushing the Supreme Court into uncharted waters. They also note that, however many Catalan politicians are tried and convicted, imprisonment is not a viable alternative to a political solution that Mr. Rajoy has failed to reach.
Mr. Rajoy dissolved the parliament of Catalonia, which represents one-fifth of the Spanish economy, and called new elections in December, which served only to confirm the profound split in Catalan society. Mr. Puigdemont and other separatists retained their narrow parliamentary majority, with almost exactly the same share of votes — 47.5 percent — as two years earlier.
“It seems absolutely counterproductive to use criminal law and this court to solve a politico-constitutional conflict,” said José Antonio Martín Pallín, a former judge of the Supreme Court.
Since Friday’s court decision in Madrid, protesters have been back on the streets of Barcelona and other cities. Roger Torrent, the pro-independence speaker of the Catalan Parliament, is pushing for lawmakers to elect Mr. Puigdemont in absentia, though the former president has recently said he is no longer a candidate; opposition lawmakers want Mr. Torrent to resign, instead.
Separatist lawmakers have two months to form an administration or force new elections.
“Puigdemont’s arrest does not bridge the divisions between secessionist parties over what to do next,” Antonio Barroso, a political analyst at consulting firm Teneo Intelligence in London, wrote in a note on Monday.
The politics of Spain have also shifted: Mr. Rajoy now leads a minority government, and his center-right People’s Party finished last in the Catalan election. He risks being outflanked by a center-right party, Ciudadanos, that was founded on an anti-secession platform and won the most votes in Catalonia in December.
“One can be critical of the leaders on both sides and how they have handled every part of this conflict, but I don’t think this should be seen through the lens of a conflict between the rule of law and democracy,” said Alan Solomont, a former United States ambassador to Spain who is now dean of the Tisch College of Civic Life at Tufts University. The better lens, Mr. Solomont argued, was that “Catalonia is a region, subject to the Spanish Constitution of 1978, and a national government always has the right to enforce national law.”
In 2014, Catalonia’s government defied Madrid by staging a nonbinding vote on independence. Catalonia’s leader at the time, Artur Mas, was later barred from office for organizing an unconstitutional vote.
In October, Spain’s attorney general decided to prosecute Catalan leaders for rebellion, though Spain’s legal code had been revised to emphasize violence as a component of rebellion. The crime carries a maximum prison sentence of 30 years.
The Spanish authorities are also widening the investigation, looking into Catalan media executives and officers in the region’s autonomous police force, and raiding offices in search of evidence linked to the referendum last October. So far, their findings fill 15,000 pages of police reports.
Javier Ortega, a leader of Vox, a small far-right party, described the drive for Catalonian independence as ”a failed coup d’état, led by people who had already set up all the structures of a parallel state.”
Vox is a fringe party. But in his ruling last week, Judge Llarena drew a thinly veiled comparison between last year’s events in Catalonia and an aborted military coup in Spain in 1981.
Mr. Puigdemont, who had traveled to Finland, left that country on Friday, driving across Scandinavia, with officers of Spain’s secret service following him. He was detained after crossing into Germany, whose criminal code, Spanish authorities believe, will allow for his extradition.
Christian Mölling, the research director of the German Council on Foreign Relations, said he saw no reason Mr. Puigdemont would not be extradited to Spain.
“If we pass this onto politics, it would be a declaration of bankruptcy for the judiciary,” he said. “We have courts precisely to depoliticize things.”
Because of an editing error, an earlier version of this article misstated the sentence given to Artur Mas. He was fined 36,500 euros and barred from holding public office for two years, but not imprisoned.
Because of an editing error, an earlier version of this article misstated the given name of Spain’s prime minister. He is Mariano Rajoy, not Mario.
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