Hi Jim and welcome to the forum.
For simplicities' sake I would "register" the boat in the US. I put quotes around register because there are two ways to do this. You can register the boat in a state like CO or you can do a federal "registration" through the USCG that is correctly called documentation
For larger, cruising boats by far the most common is USCG documentation
but this is a bit more complicated, especially for the first time a boat is documented. In addition to registering the boat it also shows clear title or any liens like bank loan or mortgage, unpaid yard bills against the boat, etc.
Both options have been covered in great detail in numerous previous discussions. Quick check with the CF search function will find you hours of reading on the pros, cons and details of both. One thing you will need to deal with will be state sales tax which can be totally different depending on the state where you reside, where you keep the boat in the US if you ever do or where you choose to pick as the hailing port for the USCG documentation.