It seems the answer to that is "not yet"
"Police said in a statement earlier about the death of George Floyd: "As additional information has been made available, it has been determined that the Federal Bureau of Investigation will be a part of this investigation."
Speaking to US media on Tuesday, Chief Arradondo said the force's policies "regarding placing someone under control" will be reviewed as part of the probe.
According to the Associated Press news agency, Minneapolis police officers are allowed under the department's use-of-force policy to kneel on a suspect's neck as long as they do not obstruct the airway.
Asked about the FBI's involvement, Chief Arradondo said he made the decision to include the agency after receiving "additional information" from a community source "that just provided more context".
In a statement, a spokesperson for the FBI Minneapolis division said the agency's investigation woud focus on whether the police officers involved "willfully deprived the individual of a right or privilege protected by the Constitution or laws of the United States".
When completed, the agency will present its findings to the Minnesota state's attorney for possible federal charges. The Minnesota BCA, which investigates most in-custody deaths, will continue to conduct its own investigation, focusing on possible violations of state laws."