As I said I work at the VA in Madison...citing Federal law below...and yes this includes the parking areas...
TITLE 38 - PENSIONS, BONUSES, AND VETERANS' RELIEF
CHAPTER I - DEPARTMENT OF VETERANS AFFAIRS
PART 1 - GENERAL PROVISIONS
1.218 - Security and law enforcement at VA facilities.
(13) Weapons and explosives. No person while on property shall carry firearms, other dangerous or deadly weapons, or explosives, either openly or concealed, except for official purposes.
(b) Schedule of offenses and penalties.
(37) Possession of firearms, carried either openly or concealed, whether loaded or unloaded (except by Federal or State law enforcement officers on official business, $500.
Reference-
38 USC Sec. 901
Sec. 901. Authority to prescribe rules for conduct and penalties
for violations
(a)(1) The Secretary shall prescribe regulations to provide for
the maintenance of law and order and the protection of persons and
property on Department property.
(2) In this chapter, the term "Department property" means land
and buildings that are under the jurisdiction of the Department and
are not under control of the Administrator of General Services.
(b) Regulations under subsection (a) shall include -
(1) rules for conduct on Department property; and
(2) the penalties, within the limits specified in subsection
(c), for violations of such rules.
(c) Whoever violates any rule prescribed by regulation under
subsection (b)(1) shall be fined in accordance with title 18 or
imprisoned not more than six months, or both. The Secretary may
prescribe by regulation a maximum fine less than that which would
otherwise apply under the preceding sentence or a maximum term of
imprisonment of a shorter period than that which would otherwise
apply under the preceding sentence, or both. Any such regulation
shall apply notwithstanding any provision of title 18 or any other
law to the contrary.
(d) The rules prescribed under subsection (a), together with the
penalties for violations of such rules, shall be posted
conspicuously on property to which they apply.
(e) The Secretary shall consult with the Attorney General before
prescribing regulations under this section.