What if David Sweat was doing time for check fraud? Would shooting him still be legal?

Specifically, if the state were still New York, and David Sweat had committed a non violent crime and had run away from prison, would it still be legal for the searchers hunting for him to shoot? The officers who shot him stated that he was about to disappear into a treeline where they might lose sight of him, realistically probably for only a short period. Presumably, they would have soon found him again - with 1200 cops, dogs, and IR cameras, it doesn’t seem probable that he would stay clear of them for long.

What about other states?

I suspect the escape was a felony.
See “fleeing felon”.

See my answer here.

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