Your question would include most and no doubt all states. Every state is different. The most common laws prohibit certain exotics, potential nuisance species, and venomous. States often have laws about exporting native species as well so one state might prohibit a species due to its illegal exportation from another state. There are laws in place that facilitate the cooperation between states. Also county and municipalities often have laws that prohibit certain reptiles. Sub state jurisdiction can have any laws they wish as long as they meet or exceed, and do not contradict state laws.
The only real way to address your question is to research a specific locality. Start at the State level and then check with the local jurisdiction. Each State is different as to what agency has jurisdiction over reptile legislation and enforcement. There is a book out on reptile laws though some states have altered their legislation since the book was last published. It is still a good starting place.
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Randy Hallman
Firehouse Herps