A set of principles devised during a meeting of charity officials in Charleston, South Carolina, called the Charleston Principles, addresses the issue of internet solicitation. The State of Connecticut has not legislatively adopted the Charleston Principles, but we do abide by them.
If a organization is located in Connecticut and only solicits via the internet (donate button on website) it needs to register in CT.
If an organization is located outside of Connecticut and only solicits via the internet (donate button on website), it does not need to register. This assumes that a resident of Connecticut comes across the out-of-state's website online; the organization did not direct the resident to the website.
For example, a Connecticut resident wants to help dolphins and searches the internet for a group that helps dolphins. If the organization that the resident chooses is located outside of CT, the organization does not need to be registered in the state, just because a Connecticut resident found their website. However, if the out-of-state charity decides to contact this Connecticut resident for another donation, or otherwise solicits a resident of Connecticut, it will need to register before doing so.