DC Personal Protection Reciprocity Act This bill declares that the prohibitions of the District of Columbia Official Code against carrying a pistol within Washington, DC either openly or concealed without a license under DC law shall not apply to an individual who is: not prohibited by federal law from possessing, transporting, shipping, or receiving a firearm; carrying a valid license or permit for a concealed firearm issued under the law of a state; and carrying a valid identification document containing the individual's photograph. The Metropolitan Police Department, upon application by a person with a bona fide residence or place of business within the United States and a license to carry a concealed pistol under the law of any state or local government, shall issue that person a license to carry a concealed pistol within DC for up to two years from its date of issue, regardless of the applicant's reason for applying for the license. The bill repeals the condition on the permission for a non-DC resident who lives in a state that does not require a license to carry a concealed pistol to apply to the department for a license to carry one within DC for up to two years. The condition repealed states that the non-resident may apply for a license to carry a concealed weapon only if the non-resident meets the same reasons and requirements a person must meet who has a bona fide residence or place of business in DC. The department shall enter into reciprocity agreements with each other state that requires such an agreement in order to grant recognition to a license to carry a concealed firearm issued by that state.