"Duty to act" is a well-defined idea in most places for emergency responders.
In New York State, police and firemen have an unqualified duty to act: if you're on shift or off, and you see a crime/a fire, you are obligated to do something about it or you're criminally liable. If you're an EMT, duty to act only pertains if you're on duty -- but if you initiate care, you are subsequently bound and liable if you abandon your patient.
For EMS, sure. For law enforcement officers, their only duty is to "the public at large". They are not liable if they let an individual die. (Regular civilians have this right, too, in most jurisdictions)
in new york, anyway, it's the other way around. Here are the examples we were given in EMT training:
If you're an off duty cop at a convenience store getting a slurpee at 3 AM, and the guy in line in front of you robs the place, and all you do is stand there, you are (potentially) liable. In practice, enforcement is pretty lenient here, especially if you don't have a service weapon on you, but you're legally required to make at least a token effort.
If you're an EMT in the hypothetical 7/11 with your slurpee and not on shift (or, i believe, in uniform) and the guy in front of you keels over from a massive heart attack, you can stand there and watch him die and nobody can touch you. IF you touch him (and start chest compressions or whatever), now you can't leave until you hand him off to an ambulance crew or someone more medically qualified than you. If you _are_ on shift, you must act no matter what.
There are additional complications for volunteer EMTs versus paid EMTs that don't pertain here but relate to at which points which legal statutes cover you or don't.
Most of the "no duty to act" precedent revolves around normal cops on patrol who witness crimes and don't stop them or who don't show up expediently when a crime is called in. Being tasked with securing a school likely establishes a specific duty do do that job regardless of whether or not there's other state law establishing that duty.
In New York State, police and firemen have an unqualified duty to act: if you're on shift or off, and you see a crime/a fire, you are obligated to do something about it or you're criminally liable. If you're an EMT, duty to act only pertains if you're on duty -- but if you initiate care, you are subsequently bound and liable if you abandon your patient.