...AFAIK, the matter of using (or lack of thereof) military to help civil forces during crisis was a key point of post-Katrina uproar.
The problem is that use of the military for law enforcement is restricted by the Posse Comitatus Act. Essentially,
Federal military forces cannot be used for civil law enforcement (this also includes Army Reserve and Air Force Reserve units), nor can State military forces be used if called up by the
Federal Government. State military forces are Guard units (Army National Guard, Air National Guard). Only State National Guard troops can be called up for civil law enforcement, and only by the State (not the Federal government). Also, the Coast Guard is excluded from the Posse Comitatus Act, and can freely be used for civil or federal law enforcement.
I do believe that, eventually, the Louisiana National Guard was called up to augment civillian law enforcement after Katrina. Only the Louisiana State Government had the authority to call up National Guard troops for this purpose. Both FEMA, and The Department of Homeland Security were/are forbidden by law (the Posse Comitatus Act) to do the same. AFAIK, Coast Guard and other federal military assets/units were only used in a search and rescue role, for medical facilities, and for bringing in relief supplies.
However, use of Military Forces in a law enforcement capacity on a Federal Reservation (specifically, a stateside US Military Base) is another story entirely. Overseas though, it depends upon the SOFA agreement with the host country (depending on whether it's a "closed" or "open" base, whether the base is leased and under US management or the US military is only a "tenant" on a host nation base, etc.).
Robbing a bank on a Federal Reservation though, seems an extremely foolish thing to me. Most bases would probably have equipment and weapons, not to mention the training Cor_Malek spoke of, that civil law enforcement can only dream of. A little off topic from the thread, but a cool story: I heard a story once while TDY at Hurlburt Field (Florida) about a robbery on neighboring Eglin AFB. Apparently the Eglin bank or credit union was broken into during the night, and the robber(s) attempted to flee the base through a large undeveloped forest area (Eglin is a HUGE base, with Hurlburt Field connected but essentially a separate installation). Military Law Enforcement (LE) lost the robber(s) in the woods, so they requested a helicopter from neighboring Hurlburt. Hurlburt Field just happens to be Air Force Special Operations Command Headquarters. The helicopters they had at the time were special operations versions of the H53, designated MH-53J PAVE LOW. Along with standard night vision equipment, they also have a Forward Looking Infrared (FLIR) system - an extremely good infrared camera and display system - and an Infrared spotlight (the light is invisible to the naked eye). Basically they can fly virtually invisible at night (except for rotor/engine noise) and literally see in the dark. They sent the helicopter in to find the robber(s), which apparently didn't take very long, and called in the LE's to scoop them up. If they had needed to, they probably could have just pinned them down using their rotor wash (a 53 is
not your standard helicopter - 6 rotor blades compared to the 2 that most police helicopters might have - and enough power/lift to pick-up a HumVee!). I honestly don't know if the helicopter was armed at the time, but if it had been, and the robber(s) had attempted to shoot at them, it would have been a very bad day for the bad guys. A 53 can carry a combination of .50 cals and 7.62mm mini-guns, not to mention small arms the crew could carry and employ.
The fool(s) never had a chance!
