The USPS has the rights to ban arms within their buildings. But what about banning them if they are in the vehicle you parked at their site?
Well they think they have that right but a judge told them "No".
The news coverage below is from November 2011 when they began with their lawsuit.
From FOX News: (7/11/13)
A federal judge has reportedly ruled that a U.S. Postal Service regulation banning firearms in its parking lots violates the Second Amendment.
The Denver Post reports that Senior U.S. District Judge Richard Matsch said the Postal Service does, however, have a right to bar Tab Bonidy — a Colorado man who filed the lawsuit in U.S. District Court in Denver along with the National Association for Gun Rights — from carrying his gun into the Post Office building itself.
Bonidy has a concealed carry permit and routinely carries a firearm, the newspaper reports. In 2010, Bonidy’s lawyer sent a written inquiry asking if he would be prosecuted under the USPS regulation if he carried his gun into the Post Office or stored it in his vehicle in the public parking lot when picking up his mail, according to Matsch’s ruling.