Did some research and found that they were semi-privatized. While this doesn't answer the question of whether or not the building is federal property, it does shed a little light on the federal status of USPS.
"The United States Postal Service® is an independent establishment of the Executive Branch of the United States Government. It operates in a businesslike way." -http://www.usps.com/postalhistory/welcome.htm
as for whether or not they are federal property, I haven't found anything to that effect as of yet.
Edit: Wiki says that the fleet of vehicles are privately maintained, so I would assume that the buildings would be also?