i might be mistaken here, so please double check--i wrote down all of the laws a little over a year ago, but some may have changed since.
ohio: as long as you do not have crotalus h. horridus (timber rattlesnake) or sisturus catanatus (eastern massauga), you have nothing to worry about.
kentucky: nothing to worry about at all.
tennessee: you cannot have sisturus miliarus streckeri (western pygmy rattlesnake).
north carolina: numerous protected species--crotalus adamanteus (eastern diamondback), crotalus h. horridus (timber), crotalus h. atricaudus (canebreak), sisturus m. miliarus (carolina pygmy), and micrurius fulvius (coral snake)
south carolina: no problems here.
georgia: requires a permit to possess exotic venomous...you may want to plan an alternate route, or just be really careful driving through georgia.
again, these were all over a year ago, so you may want to check with each state individually just to make sure.
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currently have:
boids:
1.1 ball pythons (snake'n'bake, sally)
1.0 reticulated python (mousetrap)
1.0 children's python (a***ole)
1.0 macklot's python (shaft)
1.0 cook's tree boa (cookie)
colubrids:
1.0 leucistic texas rat (ice)
0.1 everglades rat (flame)
1.0 eastern coachwhip (waco)
1.1 corn snakes (on the cob, creamed)
1.0 albino striped cal king (183)
0.0.1 mangrove (fonzie)
venomous:
1.0 western diamondback rattlesnake (elvis)
0.1 albino monacled cobra (spot)
0.1 cottonmouth (elizabeth)
1.0 gaboon viper (muffin)
0.1 pope's pit vipers (cyclops)
lizards:
1.0 nile monitor (dick)
0.1 blue tongue skink (skinky)
1.1 mali uromastyx (archie, edith)
0.1 monkey tail skink (skinky v)
0.1 bearded dragon (stump)
turtles/tortoises:
1.0 common snapper (snapple)
0.0.1 sulcata (tortle)
inverts:
0.0.? black widows
0.0.1 deathstalker scorpion (fredo)