Can a city or state police officer carry a gun at government(federal) property?
It depends on the government property. Most government property is “joint jurisdiction”, or “concurrent jurisdiction” (same thing), meaning both federal and state laws cover the property, and as such an officer (state or city) with jurisdiction can carry what is allowed by law (as in most, but not all cases). Go to the white house and you will find even federal agents are not allowed to carry a weapon outside of the Secret Service.