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?
You can not realistically ask municipal emergency responders to sign an NDA before entering your facility.
However, you may be able to form your own police department, fire department, etc. - depending on laws in your jurisdiction. Then it is your department, and you can NDA the staff if you want. Negotiate with your municipality. I am sure they will be relieved to no longer be responsible for your facility.
Your NDA would be without force.
To have a binding contract - and an NDA is a contract - both sides do need to get consideration - which means something of value, even a mere peppercorn. But the allowance to enter and save someone else is not consideration. Non-private Emergency services in most modern states are under protective laws that grant a blanket allowance to trespass, knock down doors and if needed even bulldoze cars out of the way so they can get places to help people, so your NDA don't even offer them anything.
On the other hand, you demanding the NDA could be seen as hindering the emergency services, which - depending on the jurisdiction - can make you liable for damages to the person already damaged (by virtue of delaying the access of the emergency service) or by virtue of breaking a specific law.