Well, you need more specifics, what kind of ammunition, bb or .177 cal. (commonly confused), co2 or spring loaded firing mechanism, the guns FPS (if possible), and the small animal hypothetically intended to be killed.
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No animal can kill a kodiak bear except a human with a good hunting rifle.
Depending on the size of the animal. Then yes it can with a good head shot. If the animal is too big it may not kill it, and then you have one very mad animal at you.
Rodents and small birds
I don't see why not if the animal is being a pest or nuisance.
Yes it can, since it is a small animal.
Rodents and small game.
Yes, small game and rodents.
Rat poison can kill any small animal , but if a large animal contains the poison with a certain amount it will possibly kill or injure the possessor. Rat poison can also kill babies or small children.
any air rifle that fires a .177 pellet over 600 FPS should be sufficient
Yes a C9a can be used to kill small game. The kill ratio is up to you and how good a shot you are. The best shot is a head shot with hunting pellets for a quick kill.
Very small rodents. The rifle was designed for target practice and plinking not hunting.
What couldn't you kill with a rifle of any kind? Of course you can kill a hog with an 8mm.