Darry ,
I can't find any mention of pellet or air rifles in the hunting regulations. What I did find about taking game is posted below.
You could also contact the Nebraska Game and Parks Commission
http://www.ngpc.state.ne.us/admin/contact.aspLEGAL METHODS OF TAKE
Small Game, Upland Game and Migratory Game Birds
SHOTGUN: Only 10 gauge or smaller may be used for all game birds. For waterfowl and other migratory game
birds, including doves, shotguns must be plugged to limit shell capacity to no more than three shells in the chamber and magazine combined. No plug is required for upland game birds. No plug or gauge restriction exists for cottontail rabbits and squirrels.
RIFLE OR PISTOL: Illegal for all game birds.
BOW AND ARROW: Legal for rabbits, squirrels, and upland game birds. Legal for turkey with a special permit (see the fall and spring turkey
brochures for turkey permit information). Legal for migratory game birds.
CROSSBOW: Legal for rabbits, squirrels, upland game birds except turkey (see the 2008 fall turkey brochure for turkey permit information).
NOT legal for migratory game birds.
TRAPPING: Legal for furbearers, cottontails, jackrabbits and squirrels during open seasons.
FIREARM RESTRICTIONS
During the nine-day November firearm deer season, wild animals other than deer may be hunted only with a shotgun, .22 rimfire rifle, .22 rimfire
handgun, or a smaller caliber rimfire rifle or handgun. Only hunters with valid (unfilled) firearm deer permits may hunt other animals with a centerfire rifle or centerfire handgun during the firearm deer season