PHOENIX (AP) — A federal judge refused Friday to require that Arizona officials count ballots by hand in November, dismissing a lawsuit filed by the Republican nominees for governor and secretary of state based on false claims of problems with vote-counting machines.

Kari Lake, who is running for governor, and Mark Finchem, a secretary of state candidate, won their GOP primaries after aggressively promoting the narrative that the 2020 election was marred by fraud or widespread irregularities.

Their lawsuit repeated unfounded allegations about the security of machines that count votes. They relied in part on testimony from former President Donald Trump’s supporters, who led a discredited review of the election in Maricopa County, including Doug Logan, the CEO of Cyber Ninjas, who oversaw the effort described by supporters as a “forensic audit.”

U.S. District Judge John Tuchi ruled that Lake and Finchem failed to show any realistic likelihood of harm and that their lawsuit must be brought in state, not federal, court. He also ruled that it is too close to the election to upend the process.

“The 2022 Midterm Elections are set to take place on November 8,” Tuchi wrote. “In the meantime, Plaintiffs request a complete overhaul of Arizona’s election procedures.”

Finchem and a spokesman for Lake, Ross Trumble, said in text messages that they hadn’t seen the ruling and weren’t prepared to comment.

The lawsuit was filed against Secretary of State Katie Hobbs, the Democratic nominee for governor, and the elected supervisors of Maricopa and Pima counties, who oversee elections in the Phoenix and Tucson metro areas.

Lawyers for Lake and Finchem said hand counts are the most efficient method for totaling election results. They said the lawsuit wasn’t about undoing the 2020 presidential election results in Arizona, but rather about the upcoming election.

Election administrators testified that hand counting dozens of races on millions of ballots would require an extraordinary amount of time, space and manpower, and would be less accurate. They said extensive reviews have confirmed that vote-counting machines in Maricopa County are not connected to the internet and haven’t been hacked.

Federal and state election officials and Trump’s own attorney general have said there is no credible evidence the 2020 election was tainted. Trump’s allegations of fraud were also roundly rejected by courts, including by judges he appointed. A hand recount led by Cyber Ninjas in Maricopa County found no proof of a stolen election and concluded Joe Biden’s margin of victory was larger than the official count.

The Maricopa County Board of Supervisors, which is controlled 4-1 by Republicans, asked the court to sanction attorneys for Lake and Finchem and force them to pay the county’s legal fees. The attorneys should have known their complaint was based on frivolous information, wrote Emily Craiger, a lawyer for the county.

Lake, Finchem and their lawyers used the court “to further a disinformation campaign and false narrative concerning the integrity of the election process,” she wrote.

The lawyers for Lake and Finchem responded that their claims are “legally sound and supported by strong evidence.” Their brief was signed by attorneys Andrew Parker of Minneapolis, Kurt Olsen of Washington and Alan Dershowitz, a well-known former Harvard Law School professor.

The judge did not rule on the request for sanctions.

Attorney General Mark Brnovich says there’s no evidence that lots of dead people voted in Arizona’s 2020 election, shooting down one of the biggest claims to come out of the Cyber Ninjas’ controversial election audit.

And, in a letter addressed to Senate President Karen Fann, R-Prescott, Brnovich indicated some of the allegations were laughably implausible. “Our agents investigated all individuals that Cyber Ninjas reported as dead, and many were very surprised to learn they were allegedly deceased,” the letter states.

In addition to the 282 individuals that Cyber Ninjas claimed voted on Nov. 3, 2020 but were dead before Oct. 5 of that year, the AG’s office looked at hundreds more complaints of dead voters and a report that listed thousands of dead registered voters – but didn’t allege that ballots had been cast on their behalf.

Some of the claims “were so absurd the names and birthdates didn’t even match the deceased, and others included dates of death after the election,” Brnovich’s letter states.

The document says that one of the 282 people listed in Cyber Ninjas’ allegations was found to be “deceased at the time of the election” and that other claims “resulted in only a handful of potential cases.” Asked for details on the small number of potential cases, AG spokesman Ryan Anderson pointed to a list that shows three “dead voter” cases stemming from the 2020 election – all previously-reported cases of individuals who improperly cast a single ballot that was intended for their deceased parent.

The AG’s office apparently invested “hundreds of hours” investigating the claims and is now ready to close the books on claims about dead voters, but the letter also cautions that the wider election case isn’t finished yet: “The work of the Attorney General’s Election Integrity Unit remains ongoing.”

The letter, dated Aug. 1, comes the day before a GOP U.S. Senate primary that Brnovich looks poised to lose, according to recent polling.

That, according to GOP consultant Barrett Marson, was probably a factor in Brnovich deciding to release the letter now. If Brnovich thought he stood a chance, he wouldn’t have put it out now, Marson said. (Marson is also working for a PAC supporting Blake Masters, one of Brnovich’s opponents in the Senate primary.)

Anticipating a primary loss, Marson said, the letter could be a preemptive attempt to head off criticism.

“I think this was done so that the criticism of ‘he waited until after the election’ can’t materialize. But let’s face it, a day before the election – it’s not much of a distinction,” Marson said.

The letter represents the latest shift in Brnovich’s messaging on election fraud claims. After initially shooting down election conspiracy theories in the days after the 2020 election, Brnovich slowly changed his stance last year, as his Senate campaign took shape.

This April, following months of intense pressure from former President Trump to “do his job” and find that the 2020 election was “a total fraud,” Brnovich issued an extraordinary interim report that catalogued a long list of “vulnerabilities” in Arizona’s election system, but didn’t contain any evidence of widespread fraud.

Brnovich’s Aug. 1 letter, despite using some bold language to reject the allegations about scores of “dead voters,” also assured Fann that he took the reports seriously.

“We supported the Arizona Senate’s ability to conduct an audit of Maricopa County’s elections and understand the importance of reviewing the results. However, allegations of widespread deceased voters from the Senate Audit and other complaints received by the EIU are insufficient and not corroborated,” he wrote.

The issue the letter addresses pertains not only to the Senate race, but also to Republican primaries from the governor’s race to local legislative contests. Races for the GOP nomination for governor, secretary of state, attorney general and several legislative offices feature candidates who deny the results of the 2020 presidential election.