The correct alternative is: "A hospital would be included in the Public Safety Service".
The Department of Public Safety is a government agency which has some responsibilities to the population, including: Fire services, Rescue services, Ambulance and Emergency Medical services, Security Guard licensing services, and so on.
As stated above, it's the Department's responsibility to provide Rescue, Ambulance and Emergency services for the population, which means a Hospital would indeed be included in the public safety service.
On the other hand, it says nothing about Libraries, Elections or Treaties.