Costco Wholesale Corp. won’t have to face consumer claims that it overcharged customers sales tax in New York when they used coupons, the U.S. Court of Appeals for the Second Circuit affirmed June 12.

New York law requires that claims over unlawful collection of sales tax be brought in a state administrative proceeding.

The consumer here can’t make an end run around the exclusive remedy for these claims and pursue them in court, the appeals court said in an unsigned...