An immigration officer facing state charges in connection with a shooting in Minneapolis was released from jail on Thursday after Republican officials in Texas prevailed in an extradition battle with their Democratic counterparts in Minnesota. It is unclear whether the agent will ultimately answer those charges in court.

The officer, Christian Castro of Immigration and Customs Enforcement, had been jailed for the last three months in Cameron County, Texas, while Minnesota officials sought to have him sent north to face assault charges related to a shooting in January that wounded a Venezuelan immigrant.

Sheriff Manuel Trevino of Cameron County said Mr. Castro was released just before 7 a.m. local time.

The case has tested the limits of state powers in an era of deep political mistrust.

It is rare for federal agents to face state criminal charges for on-duty conduct, and the Trump administration has argued that the charges Minnesota prosecutors have filed against Mr. Castro are illegitimate. It is also exceedingly rare for one governor not to act on a request from another to extradite a criminal defendant, as Gov. Greg Abbott of Texas has done.

Because Mr. Castro did not agree to leave Texas, where he lives, Minnesota officials needed Mr. Abbott to approve a request to extradite him. But Mr. Abbott, a Republican, has so far declined to act on the request from Gov. Tim Walz of Minnesota, a Democrat. Because Texas law limits detention in extradition cases to 90 days, Mr. Castro had to be freed on Thursday.

Minnesota officials have said they were worried that Mr. Castro would flee to Mexico if he was released, and they filed a lawsuit asking a federal judge to force the Texas governor to act. But Mr. Abbott’s lawyers said he needed more time to determine whether Mr. Castro was eligible for extradition. The judge sided with Texas on Wednesday, finding that there was no proof that Mr. Abbott was acting in bad faith.

Mr. Castro was among the thousands of federal agents sent to Minnesota last winter as part of the Trump administration’s immigration crackdown, which resulted in violent clashes between agents and residents, thousands of arrests and three shootings.

Mr. Castro was accused of shooting a Venezuelan man, Julio C. Sosa-Celis, on Jan. 14 after a long car chase and short foot pursuit with Mr. Sosa-Celis’s roommate.

State prosecutors said Mr. Castro fired through the door of a home, striking Mr. Sosa-Celis in the leg. They charged Mr. Castro in mid-May in state court in Minneapolis with four counts of assault and one count of falsely reporting a crime.

Mr. Castro, who returned to Texas shortly after the shooting, did not travel to Minnesota to face the charges. He was arrested in Texas in late May on a warrant from Minnesota.

Mr. Castro has not publicly addressed the charges against him, and he did not respond to requests for comment through a jail messaging system in recent months.

In the immediate aftermath of the shooting, federal officials backed Mr. Castro and accused Mr. Sosa-Celis and his roommate, who is also from Venezuela, of engaging in a sustained attack with a broom and a shovel.

Days after the shooting, Mr. Sosa-Celis and his roommate were charged in federal court with assaulting a law enforcement officer. But federal prosecutors dismissed that case in February after investigators determined, based on a video of the encounter, that agents had likely lied about the events that led to the shooting.

Federal officials have said they were investigating the agents involved in the shooting, though no federal charges have been announced.