WASHINGTON — A federal appeals court on Tuesday overturned a federal rule that laid out how much air pollution states would have to clean up to avoid incurring violations in downwind states.

The decision sends the Environmental Protection Agency, and perhaps even Congress, back to the drawing board in what has become a long and paralyzing argument over how to mesh a system of state-by-state regulation with the problem of industrial smokestacks pumping pollutants into a single atmosphere.

In a 2-to-1 ruling, a panel of the United States Court of Appeals for the District of Columbia said the E.P.A. had exceeded its authority in the way it apportioned the cleanup work among 28 upwind states.

The agency was trying to address a problem that has vexed the air pollution control system for at least three decades: how to deal with states whose own air meets standards but whose power plants, refineries and other industrial plants emit sulfur dioxide and nitrogen oxide pollutants that — wind-aided — prevent neighboring states from attaining the level of cleanliness required under federal law.