In Arizona et al. v. Inter Tribal Council of Arizona, Inc., et al., the court ruled that the federal National Voter Registration Act of 1993 — or the "motor voter" act — trumps an Arizona law that "requires voter-registration officials to 'reject' any application for registration, including a Federal Form, that is not accompanied by documentary evidence of citizenship."
While they note that Arizona has a right to decide who votes in state elections there, they are able to request changes to the federal registration form, and then challenge the federal government if it fails to incorporate those changes. The court does not rule on the merits of such a lawsuit by Arizona.
Antonin Scalia wrote the opinion, joined by John Roberts, Ruth Bader Ginsburg, Stephen Breyer, Elena Kagan, and Sonia Sotomayor. Anthony Kennedy joined in part, and wrote a concurrence. Clarence Thomas and Samuel Alito each wrote dissents.