In other words, technically, you have to pay sales tax when you buy something, and if you don't then you're supposed to pay the equivalent amount in "use tax". In this case, CT is trying to wedge in there and get tax when neither the buyer or the retailer are in CT.
It's not a business killer for Amazon to charge and pay the taxes for every state. Many on-line retailers do. There is software and subscription services to keep billing systems up to date with current tax tables. But, who pays sales/use tax on what when a guy in CA buys something from Amazon that was referred by a CT affiliate? What about when someone in a state where Amazon has no physical presence buys from Amazon through a CT affiliate? My brain hurts and I suspect someone's getting screwed.