I registered my 750 in MA with no title as well. I believe it once had one because the registration was MA, not sure, but they first tried to push me out the door, then after trying to explain that the previous owner didn't have one either, they said they would do a "title search". This involved them telling me to come back in 2 days while they called the main registry(boston), and they looked in the physical files. After nothing turned up, they would allow me to register it. I also had to get a VIN inspection at a local police station before going back. (had to print the form from the RMV website and bring with the bike in tow.) When I went back I had to find the same person who dealt with me the first time.
But being a bike from NH and no title, it shouldn't be as much as an issue. if all else fails, find a RI friend to register it there.