"美国北达科他州" can be translated as "North Dakota, the United States" or more naturally as "North Dakota (in the U.S.)" or simply "North Dakota, U.S." when the context makes it clear that you're referring to a state within the United States.
In most cases, especially in formal writing or when clarity is crucial, "North Dakota, the United States" would be a precise and unambiguous choice. However, in casual conversation or when the context is already established, the shorter versions like "North Dakota, U.S." would be perfectly acceptable.