I don't like Wiki but .....
If a person is covered by the LEOSA, then "notwithstanding any other provision of the law of any State or any political subdivision thereof," he or she may carry a concealed firearm in any state or
political subdivision thereof. See Title 18, USC, Section 921, which defines "state" to also include the
District of Columbia,
Puerto Rico and U.S. Possessions. Thus, the LEOSA-qualified person does not generally require a state-issued
permit for carrying concealed firearms.
However, there are two types of state laws that are not overridden by the federal law, these being "the laws of any State that (1) permit private persons or entities to prohibit or restrict the possession of concealed firearms on their property; or (2) prohibit or restrict the possession of firearms on any State or
local government property, installation, building, base, or park." This does not mean that LEOSA-qualified persons are prohibited from carrying concealed firearms in such areas, but only that they must obey whatever state laws apply on those two points.
They are free to disregard all other state and local laws that govern the carrying of concealed firearms.
The LEOSA overrides state and local laws, but not other
federal laws. Thus, LEOSA-qualified individuals must continue to obey federal laws and agency policies that restrict the carrying of concealed firearms in certain federal buildings and lands.