District of Columbia Financial Efficiency Act of 2013 - Amends the District of Columbia Home Rule Act to authorize a change of the District of Columbia fiscal year by an Act of the D.C. Council.

Appropriates, out of any moneys of the District of Columbia government not otherwise appropriated, and out of applicable corporate or other revenues, receipts, and funds, the amount provided for any project or activity for which funds are provided in the local budget act for such fiscal year, if as of the first day of the District government fiscal year neither the regular District of Columbia appropriation bill for the fiscal year nor a District of Columbia continuing resolution for such fiscal year is in effect.

Declares that an appropriation and funds made available or authority granted for a project or activity for a fiscal year under this Act shall be at the rate of operations provided for it under the local budget act for the fiscal year.

Terminates such an appropriation and the availability of those funds: (1) during any period of the fiscal year in which a District of Columbia continuing resolution for the fiscal year is in effect, or (2) upon enactment of the regular District of Columbia appropriation bill for such fiscal year.

Specifies restrictions on programs or activities subject to other appropriations Acts.

States that nothing in this Act shall be construed to effect obligations of the District government mandated by other law.

Increases the salary of the District's Chief Financial Officer to a rate that does not exceed the total annual compensation payable to the Vice President (currently, that does not exceed the rate at level I of the Executive Schedule).