4 U.S. Code § 7 - Position and manner of display
(m)(3)
"The flag shall be flown at half-staff 30 days from the death of the President or a former President; 10 days from the day of death of the Vice President, the Chief Justice or a retired Chief Justice of the United States, or the Speaker of the House of Representatives; from the day of death until interment of an Associate Justice of the Supreme Court, a Secretary of an executive or military department, a former Vice President, or the Governor of a State, territory, or possession; and on the day of death and the following day for a Member of Congress. The flag shall be flown at half-staff on Peace Officers Memorial Day, unless that day is also Armed Forces Day."

4 U.S. Code § 10 - Modification of rules and customs by President

Any rule or custom pertaining to the display of the flag of the United States of America, set forth herein, may be altered, modified, or repealed, or additional rules with respect thereto may be prescribed, by the Commander in Chief of the Armed Forces of the United States, whenever he deems it to be appropriate or desirable; and any such alteration or additional rule shall be set forth in a proclamation.