On page 2, it tells you what local species are able to be taken without a permit. On page 3, it states what amphibians are forbidden to be kept as pets, and that all other animals, native or exotic, require permits/licensing.
So it seems to possess tiger salamanders in Colorado, you need a license. I don't know specifically which license, but in most states it's usually just a fishing license. If I were you, I'd contact:
With wildlife questions, contact:
Colorado Division of Wildlife; Don Masden
2300 S. Townsend Ave., Montrose, CO 81401
970/252-6006
With alternative livestock, importations, humane care, or pet questions, contact:
Colorado Department of Agriculture—State Veterinarian
700 Kipling St., Suite 4000, Lakewood, CO 80215
303/239-4161
And once you know which license you need, go
here.