Reporter Nikita Stewart explains Jeffrey Thompson's significance in D.C. politics and connections to key figures. (The Washington Post)

The legal maneuvering in an ongoing federal investigation into Mayor Vincent C. Gray’s 2010 campaign has reached the U.S. Supreme Court and has the potential to prolong an already lengthy probe.

Attorneys for D.C. businessman Jeffrey E. Thompson, the alleged financier of an off-the-books effort for Gray, have appealed to the high court in a dispute over millions of pages of documents seized from Thompson’s home and offices.

A redacted copy of the petition made public this week provides a window into the behind-the-scenes legal wrangling and helps explain why there have been no public developments in the investigation in recent weeks.

The federal probe into the alleged $635,000 secret “shadow campaign” for Gray has generated uncertainty in the District’s political landscape in advance of next April’s mayoral primary. Gray (D), who has not been charged and has denied any wrongdoing, has not announced whether he will seek a second term.

The mayor said Friday on WAMU-FM that he would make an announcement “within a few weeks.”

The questions at issue in Thompson’s appeal are not directly related to the substance of the investigation into the mayor’s 2010 campaign. But the legal machinations make it more difficult for the office of U.S. Attorney Ronald C. Machen Jr. to proceed.

As long as the documents are in limbo, prosecutors run the risk that records that they have not reviewed contain information that could undermine their case. Alternatively, if prosecutors decide to rely on disputed documents in a potential case, a court could later rule they were not entitled to them.

Thompson’s petition to the Supreme Court, filed Sept. 26, asks the justices to intervene in a long-running battle over a subset of records seized during the March 2012 search. Thompson, the former owner of D.C. Chartered Health Plan and the accounting firm previously known as Thompson, Cobb, Bazilio & Associates, had argued before the U.S. District Court and the U.S. Court of Appeals for the D.C. Circuit that many of the documents went beyond the scope of search warrants.

In January, according to court documents, the U.S. Attorney’s Office reached an agreement with Thompson about how to filter out certain records protected by various privileges. The remaining dispute involves the scope of electronic documents the government is allowed to review.

“The vast majority of the seized records have nothing to do with [redacted], but relate to confidential client matters, the operation of [redacted] business, and petitioner’s personal matters,” according to the 17-page petition for review by the Supreme Court.

The petition redacts references to Thompson, but it is clear from earlier court rulings and a grand jury subpoena reviewed by The Washington Post that he is the subject of the case and a grand jury investigation into a possible conspiracy. He has not been charged with any crimes.

Thompson’s attorney, Brendan V. Sullivan Jr., did not respond to an e-mail seeking comment.

A spokesman for Machen’s office declined to comment.

Prosecutors have been trying to establish a pattern of Thompson’s alleged off-the-books political donations. Last July, his associate Jeanne Clarke Harris pleaded guilty to funneling Thompson’s money through companies she owned to fund the alleged illegal effort for Gray.

Two months ago, one of Gray’s closest political advisers, Vernon E. Hawkins, admitted making false statements to investigators and told the court he was an architect of what has become known as the shadow campaign for the mayor.

In September, newly released court documents and interviews outlined how Thompson allegedly secretly spent more than a half-million dollars on get-out-the-vote efforts for Hillary Rodham Clinton’s 2008 presidential campaign.

The Supreme Court’s docket also sheds light on the timeline of the investigation, showing that Thompson’s attorneys requested and were granted two extensions by the court to file appeals — one in July and another in August.

Justices considered Thompson’s motion to file a petition under seal last Friday and granted the motion on Monday, according to the docket. The Supreme Court will decide whether to hear the appeal after the government has responded to Thompson’s petition by Nov. 20.

Robert Barnes and Mike DeBonis contributed to this report.