That's typically a relatively simple process, but in most cases, it's better/simpler to sue in the new state fro the get go.
What if the new state were Hawaii or Alaska?
That would be an incredibly ATYPICAL situation (hence my use of the word "typically") since Hawaii and Alaska comprise only 4% of the states in the U.S. and are home to only about 6/10ths of 1% of the U.S. population. And, of course, the person who is the subject of the thread is not in either of those states.
I'm no expert, but it's my impression that getting a judgment domesticated does not normally require an in-person appearance the way winning a judgment in the first place does.
Your impression is consistent with my experience domesticating dozens, if not hundreds, of sister-state judgments (and, in one case a foreign country money judgment). However, I only say that because you used the word "normally" (much as I used the word "typically").
As long as I am right about that, it's obvious to me that the easiest and usually least expensive approach is to sue in the nearest location the law allows, and then to domesticate your judgment in the state where the defendant has wages and/or assets to collect from, if you feel it's worthwhile.
I assume it's "obvious" to you because you are not familiar with some of the difficulties that can arise with the process of domesticating a judgment, including the fact that debtor can challenge the domestication based on an allegation that the original state lacked personal jurisdiction. I did not suggest that suing in the defendant's current state of residence is ALWAYS a better option, but the burden of traveling to that state is hardly the only factor to consider.
You can also just get your judgment and then wait the defendant out, if it seems likely he or she may need to repair his or her credit at some point in the future, and even put it on your calendar to renew the judgment whenever it is about to expire.
That's about as effective as frying an egg by leaving it outside and waiting for the temperature to rise.
I was not aware that the rules for jurisdiction and venue were different for small claims court than for other courts, and in fact am having a great deal of trouble getting any results in an internet search, to see whether that IS common to many other states or unique to CT.
For starters, here are links to the relevant California and Washington statutes, and I specifically know NY has something similar (although I don't have a link handy).