Though I admit I haven’t reviewed the statutes and cases in all the other 49, and although those documents invariably look different in every one of them, the answer is you'll likely be fine. That’s because of a provision in the Constitution about one state giving “full faith and credit” to the laws of another. That means if your New Hampshire documents have been properly executed here, they’ll probably get the credit they’re due elsewhere. How’s that for our Founders thinking ahead.
One thing that will help is to have the relevant documents with you. Even if you don’t pack hard copies in your carry-on, you might have them saved on your laptop or smart phone where you could produce them in a pinch. Of course, making sure your agents have their copies will also help if the doctor needs guidance or the banker needs something from your representatives.
Let’s flip it around now. What if you had your documents prepared before you decided on the move to New Hampshire? Will they work here or do you have to start all over again? For the same reasons I just mentioned, your powers of attorney and health care directives should be fine, as long as they’re less than 8-10 years old - those documents get stale after about that point and should be updated no matter where you've been in the meantime.
Your wills and trusts should stand up, too, and age isn’t a problem there - we’ve successfully handled many of those that were 40 or more years old. However, the issue might be terminology that differs from one state to another. For example, what if you want your property to go to your siblings, but you haven’t said what happens with the share of one who predeceases you? Does that share go to the sibling’s own children - your nieces and nephews - or does it get divided among your surviving brothers and sisters? You may have intended one result, but New Hampshire law might call for the other. The best way to sort that out would be to have the documents reviewed here to make sure things will still work out the way you planned. If not, then a modest tweak may be all that’s needed. Likewise, it might be smart to provide that the governing law will be New Hampshire's, not Connecticut's any longer, as this is where all the governing will take place from now on.
By the way, if you've relocated here from another state and left your original documents with your lawyers there, it would be smart to request that they - the documents, not the lawyers - be sent to you here. It's not unusual to find that a law firm moved or a lawyer retired, and that can make tracking down the documents more challenging.