No one has been charged.

Documents from prosecutors have suggested a theory in which Mr. Walker’s campaign aides helped direct political spending by outside groups, some of them nonprofits, as part of a “criminal scheme.” Among these was the Wisconsin Club for Growth. Officials have said that Mr. Walker was not a target of the investigation. Still, the matter has clouded Mr. Walker’s political prospects and has been a matter of discussion in his race for re-election against Mary Burke, a Democrat and former Trek bicycle executive.

At a campaign event with veterans Wednesday afternoon, Mr. Walker said the federal appeals court decision changed little. “That doesn’t alter the status where we’re at,” Mr. Walker said. “It’s still something that a respected judge here in the state of Wisconsin at the state level, who has no political ties to me or anyone I’m affiliated with, has said should not go forward.”

David B. Rivkin Jr., a lawyer for the Wisconsin Club for Growth, issued a statement describing the decision as disappointing, but noting that it did not revive the investigation. “And it does not alter our resolve,” he said. “We will ask the Seventh Circuit to correct today’s mistaken decision, and we will continue to fight this abuse of government power.”

Writing for the federal appeals court panel, Judge Frank H. Easterbrook asked broad questions raised by the case about what sorts of behaviors are permitted between campaigns and outside groups.

“The Supreme Court has yet to determine what ‘coordination’ means,” he wrote. “Is the scope of permissible regulation limited to groups that advocate the election of particular candidates, or can government also regulate coordination of contributions and speech about political issues, when the speakers do not expressly advocate any person’s election? What if the speech implies, rather than expresses, a preference for a particular candidate’s election? If regulation of coordination about pure issue advocacy is permissible, how tight must the link be between the politician’s committee and the advocacy group?”