You asked for a summary of the rules or laws governing the placement of federal troops (active-duty) in a state during emergencies.

The Stafford Act allows Congress to use federal troops for disaster relief operations, but only if a state governor requests such assistance (42 USC §§ 5121 et seq.). Using federal troops deployed under this act to perform law enforcement activities is a violation of the federal 1878 Posse Comitatus Act.

The Posse Comitatus Act prohibits the Army or Air Force from performing law enforcement activities in the United States, except where expressly authorized by the Constitution or Congress (18 USC § 1385). Department of Defense (DoD) regulations apply the same prohibition to the Navy and Marines (10 USC § 375 and DoD directive 5525.5). The courts have held that the Posse Comitatus Act does not apply to guard members called to duty by the governor. This means that governors may use their own guard members or guard personnel from neighboring states to perform law enforcement functions without violating the act. Congress has also provided some exemptions to the act. One exception is the Insurrection Act (10 USC §§ 331-335).

Under the Insurrection Act, the President may, without a governor's request, activate federal troops during emergencies, and when deployed under this act, they may perform law enforcement functions within a state. Specifically, this act authorizes the President to deploy federal troops if “insurrection, domestic violence, unlawful combination, or conspiracy”:

(1) so hinders the execution of the laws of that state and of the United States within the State, that any part or class of its people is deprived of a right, privilege, immunity, or protection named in the Constitution and secured by law, and the constituted authorities of the state are unable, fail, or refuse to protect that right, privilege, or immunity, or to give that protection; or (2) opposes or obstructs the execution of the laws of the United States or impedes the course of justice under those laws (10 USC § 333).

Historically, there appears to be an aversion to using federal troops for domestic problems. But in the last 15 years, the President has deployed federal troops under the Insurrection Act in a number of cases. For example, in 1992, then President Bush invoked the act to send troops to restore order during the Los Angeles riots (which were triggered by the Rodney King verdict). The current President Bush invoked the act to place armed soldiers at airports in the wake of the September 11, 2001 terrorist attacks. (For a more detailed treatment of the subject of federal troop placement in states, see attached Congressional Research Service documents RS222666, The Use of Federal Troops for Disaster Assistance: Legal Issues by Jennifer K. Elsea and 95-964 S, The Posse Comitatus Act & Related Matters: The Use of the Military to Execute Civilian Law by Charles Doyle.)