The office of the city manager in Farmington just emailed me a copy of their policy about this. It is dated September 5, 2000, and is titled AR-00-3, "An Administration Regulation Establishing A Workplace Violence Policy and Procedure."
I have asked that office if there is a policy or regulation prohibiting citizens who are not employees from having their legally-carried firearms on city property. I hope to hear back on that tomorrow.
The question is whether a workplace policy restricting employees of a government entity can withstand the prohibition (through preemption) on cities having their own gun control regulations.