On August 22, the U.S. Supreme Court issued an order in Republican National Committee v Mi Familia Vota, 24A164. Arizona requires people filling out a voter registration form to attach proof of citizenship. This would be a birth certificate for many persons, but for others it would be a copy of naturalization papers.
The legality of this Arizona restriction is pending in the lower courts, but in the meantime, the U.S. Supreme Court says the state can enforce its law for people who want to vote for state and local office. For people willing to vote only for president and congress, during this interim period, the state cannot block them from registering even if they don’t provide proof of citizenship. That is because those persons can use the federal voter registration form, with no need for attachments.
Four justices would have blocked the state from enforcing its law, for all offices, while the case is pending.
Three justices would have let the state enforce its law, in the interim, for all voters.
Two justices said the state can enforce its law for some times of offices but not others. Here is a description of the ruling, and a copy of the ruling, from ElectionLawBlog.