F.B.I. agents arrested a Milwaukee judge on Friday on charges of obstructing immigration agents, saying she steered an undocumented immigrant through a side door in her courtroom while the agents waited to arrest him in a public hallway.

The decision to charge a sitting state court judge is a major escalation in the Trump administration’s battle with local authorities over deportations. The administration has demanded, under threat of investigation or prosecution, that local officials not impede federal efforts to deport millions of undocumented immigrants, and the arrest sent a message that the administration intends to take a harder line with those that do.

The arrest of the judge, Hannah Dugan, comes after months of rising tensions between the Trump administration and the judiciary. President Trump and his top advisers have repeatedly assailed “local judges” for halting or questioning actions taken by the administration, particularly when it comes to immigration cases.

Mr. Trump’s drive to round up and deport large numbers of migrants has also led to other disputes with federal judges, especially over his use of the Alien Enemies Act to send Venezuelans out of the country.

In the Milwaukee case, charging documents described a confrontation last Friday at Judge Dugan’s courthouse, in which federal agents said she was “visibly upset and had a confrontational, angry demeanor” when a group of immigration, D.E.A. and F.B.I. agents came to apprehend Eduardo Flores-Ruiz, a citizen of Mexico who was in her courtroom to face domestic violence charges.

According to the criminal complaint, the judge confronted the agents and told them to talk to the chief judge of the courthouse. She then returned to her courtroom.

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