There is a season for grey squirrels.
Species:
Gray Squirrel
Season Dates
Jan 1 - Feb 28
Sep 1 - Sep 30
Oct 15 - Dec 31 1/2
Also, there is the 500 ft rule, if she was closer than 500 ft (and in season) she can't do it. Plus, she needs a hunting license. A pellet gun falls under:
Sec. 26-1. Definitions. (12) "Hunting" means pursuing, shooting, killing and capturing any bird, quadruped or reptile and attempting to pursue, shoot, kill and capture any bird, quadruped or reptile, whether such act results in taking or not, including any act of assistance to any other person in taking or attempting to take any such animal.
Sec. 26-27. Licenses required for hunting, trapping and fishing. Exceptions. (a) Except as provided in subsection (b), (c), (e), (f), (g) or (h) of this section and other provisions of this chapter providing specific license exemption, no person shall take, hunt or trap, or shall attempt to take, hunt or trap, or assist in taking, hunting or trapping, any wild bird or mammal and no person more than sixteen years of age shall take, attempt to take, or assist in taking any fish or bait species in the inland waters or marine district by any method or land marine fish and bait species in the state, regardless of where such marine fish or bait species are taken, without first having obtained a license as provided in this chapter. No person under sixteen years of age shall hunt or trap, except as provided in section 26-38.
26-66-1. Behavior and actions of hunters
(a) The method of taking wild birds and wild quadrupeds by hunting shall be restricted to firearms, high velocity air guns using a single ball or pellet type projectile, and compound, long, or recurved bow. In designated areas, by special permit, the commissioner may allow the use of modified versions of air guns or archery implements to achieve wildlife management objectives. No arrow or projectile which is coated with or contains any drugs, poison or known tranquilizing substance may be used or possessed while engaged in archery hunting.
...hope that helps.