WASHINGTON—The Supreme Court on Tuesday dismissed a closely watched case involving union organizing, after concluding it had erred in agreeing to hear the case in the first place.

The court last month heard oral arguments to consider a tactic labor unions have used for decades: agreements in which an employer pledges to remain neutral with respect to a union's effort to organize its workers. The employer also may provide employee lists or other assistance. In exchange, a union may agree to refrain from picketing or criticizing...