the Code of Federal Regulations Title 39 which is named Conduct on Postal Property says No person while on postal property may carry firearms, other dangerous or deadly weapons, or explosives, either openly or concealed, or store the same on postal property, except for official purposes.
And this: United States Code (18 U.S.C. 930) that deals with firearms in federal buildings has a section that says there are certain times you can carry concealed in a federal building The lawful carrying of firearms or other dangerous weapons in a Federal facility incident to hunting or other lawful purposes.
You can also mail a long gun or shotgun. If you are an FFL you can mail handguns as well. I think it would depend on the definition of official purposes and other lawful purposes.