Wisconsin prosecutors have alleged that Gov. Scott Walker was part of a wide-ranging “criminal scheme” to coordinate the activities of conservative groups that spent millions to help him and other Republicans fend off recall efforts, according to documents released Thursday.

Walker has not been charged, and his legal jeopardy was unclear. The documents stem from a multi-county investigation blocked last month by a federal judge, a decision currently on appeal.

In a statement, the governor called the allegations of wrongdoing “categorically false.”

The disclosures mark the first time that Walker, who is running for reelection this year and mulling over a 2016 presidential bid, has been singled out for allegedly playing a direct role in what prosecutors have called a “nationwide effort” to mobilize a network of independent groups considered crucial to his recall victory. Included in the documents is an excerpt of an e-mail he sent Republican strategist Karl Rove, describing the outside operation.

Although the case turns on Wisconsin state law, it is being watched closely by politicians and campaign operatives nationwide as they try to navigate state and federal laws that ban coordination between campaigns and well-funded independent groups.

The episode has highlighted how deep-pocketed independent groups often function as de facto extensions of official campaigns, despite such laws.

The proliferation of super PACs and politically active tax-exempt groups that followed the Supreme Court’s Citizens United decision means there is now ample opportunity for such activities. Political strategists regularly hop from a candidate’s campaign to an aligned super PAC. And candidates now commonly upload unedited video footage on their Web sites so that allied outside groups can grab clips to use in putatively independent ads.

The newly released documents “draw back the curtain on what’s happening all across the country,” said campaign finance lawyer Trevor Potter, an advocate for limiting big money in politics. Nonprofit groups “are raising large amounts of money, intervening in the political process without disclosing where the money is coming from — and all of this is being done on a broad, deliberate basis.”

Proving illegal coordination, however, is not easy, and such cases are exceedingly uncommon. Several top election law experts said they could not recall a federal criminal prosecution of alleged illegal coordination in recent history.

“It’s incredibly difficult to prove,” said Brett Kappel, a Washington campaign finance lawyer. “You have to have one party provide evidence that there was actually an agreement to do something, which means either you have to have documentary evidence or one party testifying against another, which is extremely rare.”

The newly released documents, which were filed in December 2013, relate to the Wisconsin investigation that was shut down last month by a federal judge, who said the coordination did not violate election laws because the outside groups were engaged in issue advocacy, not explicit political activity. The case is now pending before a federal appeals court.

At the heart of the Walker case is the complicated question of whether independent activities that stop short of calling for the election or defeat of a candidate can be coordinated with a campaign.

The inquiry involves tax-exempt groups such as the Wisconsin Club for Growth, Citizens for a Strong America and Wisconsin Manufacturers and Commerce, which helped finance outside efforts to support Walker and GOP state senators facing recall challenges. Walker and his top aides were deeply intertwined in the operation, the documents say.

In his statement, Walker noted that “two judges, in both state and federal courts, have ruled that no laws were broken.”

“This is nothing more than a partisan investigation with no basis in state law,” he added. “It’s time for the prosecutors to acknowledge both judges’ orders to end this investigation.”

At the hub of the scheme, prosecutors allege, were R.J. Johnson and Deborah Jordahl, political consultants to the governor’s campaign. The duo allegedly helped raise money for and steer the activities of the tax-exempt groups. Walker’s chief of staff, Keith Gilkes, allegedly was involved in discussions about the coordination of outside groups during the 2011 and 2012 recall elections, according to the court filings.

The newly released documents indicate that the governor was familiar with the operation. Prosecutors allege that he was involved in fundraising for the Wisconsin Club for Growth, which was the link between the campaign and the outside operation.

The court filing quotes from an e-mail on May 4, 2011, from Walker to Rove, in which Walker appears to brag about Johnson’s role in running the coordination campaign. “Bottom-line: R.J. helps keep in place a team that is wildly successful in Wisconsin,” Walker wrote, according to the filing. “We are running 9 recall elections and it will be like running 9 Congressional markets in every market in the state (and Twin Cities.)”

Rove declined to comment. The super PAC he co-founded, American Crossroads, was not involved in the Wisconsin recall races.

The fact that Walker alluded to the outside operation in an e-mail is “mind-boggling,” said Richard L. Hasen, an election law expert who teaches law and political science at the University of California at Irvine. He added that candidates usually go to lengths to build a wall between the operations of a campaign and outside allies.

On Thursday, when asked by reporters in Wisconsin about whether he suggested to Rove that he was coordinating outside efforts with Johnson, the governor said:, “I don’t know what specifically you’re talking about. But I can’t imagine that,” according to the Milwaukee Journal Sentinel.

The case is a so-called John Doe investigation, which means it operates under unusual state secrecy rules that bar not just prosecutors from disclosing details of investigations but also witnesses and potential targets. Much of what is known about the inquiry has come from court documents released as part of a federal lawsuit filed by the Wisconsin Club for Growth challenging the constitutionality of the investigation.

Andrew Grossman, attorney for the organization and its director, Eric O’Keefe, said his clients supported the release of all the material and believe that a full reading of the documents and the underlying cases shows that there is “no violation of Wisconsin coordination regulations” and that the original “John Doe prosecutors adopted a blatantly unconstitutional interpretation of Wisconsin law” that they used to “launch a secret criminal investigation targeting conservatives.”

Patrick J. Kenney, a deputy district attorney in the Milwaukee County District Attorney’s Office, said Thursday that the office had no comment on the case.

Kenneth Gross, former head of enforcement at the Federal Election Commission who now represents Democrats and Republicans in campaign finance cases, said the issues involved in the Wisconsin case “send chills up the spine of any of those who are pushing the envelope around the question of coordination.” But, he added, “there are so many factual defenses to allegations of coordination that it will be a tough case to make, especially criminally. Proving coordination is an uphill battle for any prosecutor.”

Jan Baran, a campaign finance lawyer, called the allegation of criminal campaign coordination “one big legal stretch.”

All campaigns, he said, seek to form coalitions and gain support.

“It is ridiculous to allege that well established independent groups become ‘subcommittees’ of the campaigns they support,” Baran said. “That would turn every supporter into a campaign committee, and subject every group to reporting.”

Dan Balz, Rosalind S. Helderman and Niraj Chokshi contributed to this report.