In most cases, you cannot use the exact same Realtor for both transactions, because a Realtor must be actively licensed in both states in order to transact real estate sales, and CT Realtors are not commonly licensed in NC as well. (VA & NC, or SC & NC would be an entirely different situation).
Most major real estate firms have partner firms in other states, or are part of national relocation networks, so you CAN work with the same real estate COMPANY, just maybe not the same Realtor. For example, I have been doing inbound and outbound relocation for a decade, and I can assist clients with the sale of their home in another state, or with locating a new home in another state, through our national network of real estate partner firms. I keep up with their needs and make sure they're getting the assistance they need through regular check-ins with the out-of-state agent who is working with them as a result of my referral.
I would be happy to talk more about your plans and how I can help you as you make this exciting transition! Please do not hesitate to reach out to me with questions or for advice...I'm always here to help!
Good Luck, and we'll look forward to having you in Raleigh soon! :)