You may own Tarantulas and so forth, but you may not buy them in CT
You also may not cross state lines with any animal without first getting an import / export permit.
The laws are very outdated and to be honest very rediculouse!.
As no one gets said permits, and people just go into RI or Mass to buy said Arachnids. But their is no "spider patrol" we are allowed to keep as many as need be as we are the ones who take the arachnids from the state, IE through seizes, or when people call local zoos / museums to get rid of the ones that they have. etc
Hope that helps a little
Thanks
Rusty