This is the situation for state employees in the state of Utah (Department of Transportation employees specifically).
Several years ago the legislation was passed...'no weapons of any kind on any state property' This included locked in your private vehicle in employee parking lots. This of course ended up in the Utah Supreme Court and was soundly defeated.
What has transpired since--if you can legally own and posses a firearm, then you can have/transport it on state property and vehicles, if all laws regarding firearms are complied with (loaded, legally loaded, concealed, open carry, no firearms posted facilities etc...).
Now each division has been given the authority to regulate weapons within their areas (within the law). In my area that means--CCW permit, you can carry concealed anytime, anywhere, except the main state HQ building that is clearly posted.
Without a permit--well, no one wants to know, or see a firearm in a state vehicle, and there is no restrictions on your private vehicle on state business.
Not too bad of a situation.
I do agree with Treo--asking an immediate supervisor for clarification would be a last resort. Try searching firearms 'Policy's and Procedures' for your state division, or other divisions that may have dealt with this issue--policies are public information.