When does "X" law enforcement agency get involved?

The Bureau of Alcohol, Tobacco and Firearms has become involved in the investigation of yesterday’s mass shooting at a sikh temple in Wisconsin, which leads me to wonder why. Presumably the local police force has jurisdiction over a crime scene - or the county sheriff, or state police if a municipality doesn’t have its own police force. But at what point is the involvement of a federal agency such as the BATF or FBI justified/authorized?

If the crime doesn’t cross state lines, the federal agencies have to be asked to investigate by the local agencies.

I learned this from an episode of Criminal Minds.

The organization and jurisdiction of the FBI, BATF (aka ATF), DEA, BOP and other various agencies of the Department of Justice can be found in Title 28 of the Code of Federal Regulations and Titiles 18 and 28 of the U.S. Code. The BATF’s general functions statement in Title 28 of the CFR will give you some idea of when they will get involved:

28 CFR 0.130 - General functions

In the case of the Wisconsin shootings, I suspect that the FBI and BATF are getting involved because the shooting is being considered domestic terrorism, because the shooter has suspected ties to neo Nazi groups linked to possible domestic terrorism, and also because of the possibilities of explosives in his home.

You said the magic word. Terrorism. Instant federal jurisdiction.

Not always true. The robbery of a federally insured bank is a US Code crime.

From memory, the federal kidnapping statute gives the FBI jurisdictional authority to investigate on thier own, IF the person is missing more than 24 hours, as then the “Presumption” is, the person has been taken out of state.

Also intrastate or foreign jurisdiction need only have a “federal element”, by statute or case law for the FBI to have jurisdiction. If a person arranges a murder by Mail, that is the federal element neccessary, as one example.