A federal judge in Arizona on Friday is set to hear a case brought by the ostensibly nonpartisan group No Labels, which is seeking to prevent its opponents from using its ballot line in the state. Should state-level candidates be able to run as No Labels candidates, it could force the self-described centrist group to disclose its secret donor list.

At the federal court at Phoenix, Judge John Tuchi will hear arguments Friday from No Labels and the Arizona secretary of state’s office. No Labels is attempting to block two candidates, for state and federal offices, who have filed paperwork to run as No Labels candidates.

The group says it only wants to nominate presidential and vice presidential candidates — not any down-ballot contenders. Should No Labels fail to block the state-level candidate, it could be forced to disclose information about who is backing its efforts, at least in Arizona.

No Labels had asked the Arizona secretary of state, Adrian Fontes, to block candidates who filed paperwork to run for state office in the fall. Mr. Fontes’s office, though, declined to do so.

The group argues that it is allowed to keep candidates from running on the No Labels line because the Constitution grants political parties “broad rights to freedom of association,” including limiting its membership and allowing for parties to choose their own candidate selection processes.

“No Labels Arizona does not intend or desire to associate with or nominate any candidate for U.S. Senator or Corporation Commissioner, or for any congressional, state, judicial, county, or precinct office,” the attorneys for No Labels wrote in their complaint. “And it does not want to have its candidates listed on the general election ballot for those offices.”

The secretary of state’s office said it is obligated to accept statements of interest — the first step candidates take when running for office — from any candidate who meets the requirements to run for that office.

In a September letter obtained by the Associated Press, the Arizona secretary of state’s office said it disagrees with No Labels’s “assertion that a newly recognized political party can choose to deprive its own voters of their constitutionally protected freedom of association.”

A spokeswoman for Third Way, a nonpartisan group opposing No Labels, Kate deGruyter, tells the Sun that No Labels is trying to act as a political party without adhering to the regulations on political parties.

“We see evidence in Arizona and nationally that the No Labels’ third-party bid is anti-democratic from top to bottom,” Ms. deGruyter says. “They are clearly acting as a political party while not playing by the rules that apply to every other registered party.”

At least one of the candidates that No Labels is attempting to block, Richard Grayson, is a perennial candidate who likens his campaigns to performance art.

Mr. Grayson is also running in the open primary to represent Alaska in the House this year. He has previously run for Congress in Wyoming, citing the law there that only requires House members to live in their districts at the time they assume office.

Mr. Grayson has taken advantage of Arizona laws in the past that allow write-in candidates to win party primaries with as few as one vote, depending on the circumstances of the race.

His decision to run for a state-level office, a utility regulator, could open up No Labels to state-level financial disclosure requirements, something the group has so far said it is not required to do because it is not running in any state-level races.

Although political parties, political action committees, and candidates are required to disclose their donors and other financial information, No Labels has been able to circumnavigate this requirement because its national organization is technically a nonprofit, not a political party.

While the national organization is a nonprofit headquartered at Washington, the state-level affiliate is a recently recognized political party.

No Labels has so far refused to disclose the identities of its financial supporters, with the group’s chief strategist, Ryan Clancy, citing concerns that it could lead to the intimidation of those supporters.

Reporting from outlets like the New Republic and Mother Jones have found that its supporters include major Republican donors, like billionaire Harlan Crow.

Such reports have added fuel to allegations from Democrats, independents, and Republicans opposed to President Trump’s re-election that the group’s true aim is to help Mr. Trump win re-election, something that No Labels denies.

“No Labels got ballot access in Arizona so we could have the option to offer it to a Unity presidential ticket in 2024. This is a one ticket, one time effort and it is well within our first amendment rights to choose not to offer this ballot line to candidates running for anything else. We are aggressively protecting our rights to choose what races we participate in,” Mr. Clancy said.