The city of Stevens Point WI has something simliar. Really odd poorly written legislation. They define "animal" as a non-human mammal, reptile or amphibian in one section, and then in another ban ownership of all "dangerous, wild or farm animals" without a permit. They define this as any animal that is not "naturally tame" or could be a threat to public safety or public property. One would think this means venomous reptiles and big cats, but its so open ended I wouldn't be surprised if someone inforced it on invertebrates.
The first thing you have to do is define the word dangerous. If you define it as something that can cause harm, then you must decide what kind of harm-causing animals you want to make illegal. In other words, the point on the dangerous scale must be decided. On that spectrum, tarantulas and centipedes fall pretty low. There are some scorpions that would be towards the top. Things like tigers are much worse than spiders. Considering we have black widows here in Ohio, banning tarantulas would be stupid, as more dangerous creatures can be found in the wild.
This was due to a mauling of a local man by a black bear on an animal sanctuary.. As stated it doesn't list T's but it doesn't exclude them and while I'm sure no one is thinking about listening anytime soon it only takes one person, with enough mouth, to start the inclusion.
Here is a local paper of mine and the article but it's on the AP general.