I am very glad you asked that:

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Headquarters of the Army,

Washington, February 12, 1861.

The following general instructions are issued for the government of the troops in this city: The several companies and detachments will have their arms and accouterments so arranged that by day or night each man can at once seize his own. The harness, guns, &c., will be so arranged as to be ready for prompt service. In case of alarm, every man will instantly proceed to his proper place; the artillery to their stables; those acting as infantry to their parade grounds. A corporal and four privates of dragoons will immediately repair to the quarters of the General-in-Chief, to bear orders. On the instant of alarm, whether by day or night, a mounted messenger from Griffin’s battery will proceed at full speed to the arsenal to notify Barry’s battery. Brooks’ company will be the guard of Magruder’s battery; Allen’s company the guard of Griffin’s battery; Haskin’s company the guard of Barry’s battery. Should the troops be suddenly called out, Magruder’s battery will at once occupy the square containing the President’s Mansion and four of the Executive Departments, a gun near each angle; Elzey’s company to occupy the Treasury building. Griffin’s battery will in a similar manner guard the General Post-Office and Patent Office. Barry’s battery will, by the shortest route, proceed to the vicinity of the Capitol, and there await further orders. Haskin’s company will join this battery. The dragoons will be held in readiness to mount at their stables. The sappers and miners will march to the front of the Unitarian Church, and there await orders. In case of alarm, outrage, or mob violence, at or near any of the public buildings or in the streets or squares of this city, Colonel Harris, Chief of the Marine Corps, will please put in rapid march to Capitol Square, there to await for further orders, as many of his marines as he can spare from other duties. Major-General Weightman, with his foot volunteers, has charged himself with the care of the bridges, including those at Georgetown. That the troops may know the officers of the staff of the General-in-Chief they will, in addition to their uniform, wear a blue scarf over the right shoulder to the left hip.

By command of Lieutenant-General Scott:

L. THOMAS,

Assistant Adjutant- General.

This order will be held in strict confidence by all of the officers who may see it, and to be shown to none but officers.

L. THOMAS,

Assistant Adjutant- General.

Official Records Series 1 Vol 51, Part 1 pg 314

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Artillery seems to be the weapon of choice.

Of interest, several of the people mentioned later became generals in the CSA army a couple months later.

Concurrent with this, Colonel Charles Stone, the Inspector General of the Washington DC militia was tasked with purging the southern sympathizers out of the local militias, a task that he was remarkably successful at accomplishing. These were the troops mentioned a General Weightman's foot volunteers. In January, there were only a few companies of militia and they were secessionist. By the time of the inauguration, they were all gone and there were several regiments worth of militia companies available. (I would have to dig for the exact numbers).