Shortly after a U.S. Immigration and Customs Enforcement officer shot and killed a woman in Minneapolis on Wednesday, city leaders began looking into whether the officer had violated state criminal law.

Minneapolis Mayor Jacob Frey said, “We collectively are going to do everything possible to get to the bottom of this, to get justice, and to make sure that there is an investigation that is conducted in full.” Police Chief Brian O’Hara followed up by saying that the state’s Bureau of Criminal Apprehension is “investigat[ing] whether any state laws within the state of Minnesota have been violated.”

If they conclude that state law has been violated, the question is: What next? Contrary to recent assertions from some federal officials, states can prosecute federal officers for violating state criminal laws, and there is precedent for that.