My dad passed intestate with ND minerals in his estate. Although we live in Texas and had an administration, we had to open and close a case in ND to establish heirship.
I assume you do not live in ND?
Since my dad did not leave a will, I cannot answer your general question about probate, but I can tell you some proceedure will have to be done in ND even if you live in another state and have probate performed. ND does not recognize probate/administration proceedings from other states. That is my understanding.
Most states will recognize "foreign" probate. That is, if you probate in your home state, all you have to do, such as in Texas, is file exemplified copies (this is more than just certified copies) in the county deed records and that's it. Too bad it's not like that in other places.
I will suggest that you consult an attorney in ND for the final word.