The company I work for has some very intense trade secret and intellectual property in its HQ. If police, fire, medical were called and needed access to certain areas of the facility were this information was kept, can the company ask that them to sign an NDA before they leave? Is it different state to state? City to city?
Yes, you can ask but if they don’t they can come in anyway. The law gives them the right to enter in certain circumstances.
Notwithstanding, any government employee that disclosed confidential information that they got in the course of their employment could be sued and possibly prosecuted.