I don't think Key West has any city ordinances against owning turtles outside of the ones already mandated by the state.
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Bill
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1.0 Banded Cal King
0.1 Striped Cal King
0.1 Aberrant Cal King
0.1 Chihuahua Mountain King
1.0 Arizona Mountain King
1.0 Anery Jurassic Milk
1.0 Nelson's/Corn snake hybrid
0.0.2 Viper Boa
1.1 Brazilian Rainbow Boa
1.0 Blue Tongue Skink
2.3 African Dwarf Frogs
0.0.1 Alligator Snapping Turtle
0.0.1 Florida Snapping Turtle
0.0.1 Loggerhead Musk Turtle
0.0.1 Common Musk Turtle
0.0.2 Fly River Turtle