Wyoming
Definitely Wyoming. Outside of city limits, you can own almost anything.
There is one single animal that you cannot own in Wyoming. It's actually on the books. You can have a fleet of Gaboon vipers, 5 Nile crocs, 3 King cobras, and a sea snake in a pear tree, if you want.
But you can't have a black mamba. I know you had your heart set on one, too.... <lol>
You can own any native--even restricted ones, so long as you have proper records of purchasing it as a captive bred animal. Of course, as anywhere, endangered species would require permits.
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Oh, and in Omaha, Nebraska:
"Pet animal: Any domestic dogs, domestic cats, mini-pigs, domestic rabbits, domestic ferrets, domestic rodents, birds except those defined as agricultural animals and specifically including any birds possessed under a license issued by the State of Nebraska and/or the United States Fish and Wildlife Service, non-lethal aquarium fish, non-lethal invertebrates, amphibians, turtles, non-venomous lizards that will not grow to more than five feet in length at maturity, nonvenomous snakes that will not grow to more than eight feet in length at maturity, or such other animals as may be specified and for which a permit shall be issued by the authority after inspection and approval; provided, however, that any animal forbidden to be sold, owned, or possessed by federal or state law is not a pet animal."
Pet animals are allowed. Essentially, Omaha has declared most herps legally domesticated. The 8 foot limit on snakes is recent--it used to be 6 feet. This is a victory for local herpers, who can now keep Irian Jaya carpets, and a variety of other species that just went a bit over the mark before. Omaha isn't stupid about it the way some places, are either--the 8 foot limit refers to the adult length of the species, and not the current size of the animal. It's a fairly liveable ordinance in my opinion.