As the nation awaits the results of a very tight U.S. Senate race between Republican Martha McSally and Democrat Kyrsten Sinema, Arizona Republican leaders were in court Thursday morning challenging which ballots some Arizona counties are counting.

The Yuma, Navajo, Apache and Maricopa County Republican parties filed a lawsuit challenging the way counties verify signatures on mail-in ballots that are dropped off at the polls on Election Day.

As of Thursday night, with an estimated 460,000 ballots still being counted around the state, Sinema held a narrow lead over McSally.

Maricopa County Superior Court Judge Margaret Mahoney ruled that counties should continue doing what they're doing, and set another hearing for 2 p.m. Friday.

Rules for checking signatures

If there is a mismatch between the signature on file and the signature on an early ballot dropped off on Election Day, Maricopa, Pima and Coconino counties are continuing to contact those voters. In phone calls, county officials allow voters to verify that they did, in fact, sign the green envelope of the ballot, as required by law.

MORE: With Arizona Senate seat at stake, Republicans sue county recorders

All three of those counties are leaning heavily in support of Sinema. The state's other counties — many of which McSally is winning — do not participate in that practice, called curing, after Election Day.

The lawsuit asked the court to require all of the counties to implement uniform deadlines for ballot rehabilitation. But it doesn't specifically say whether that means stopping Maricopa, Pima and Coconino from counting those ballots or requiring the other counties to begin curing.

Maricopa County Recorder Adrian Fontes said there are still about 5,600 ballots that need to go through curing in his county.

He's in favor of the extended curing period after Election Day and suggested that the Republican lawsuit was an attempt to invalidate ballots that should count.

"I think every eligible United States citizen who is casting a valid ballot that is verified should have that ballot count," Fontes said.

Attorneys for the Democrats in court asked that the GOP attorneys clarify what they're seeking, but the judge didn't allow for an answer.

Before the hearing, Brett Johnson, attorney for the Republicans, said the lawsuit seeks to require all counties to contact voters after Election Day so their ballots can be counted.

He said Democrats were misconstruing the complaint's intent. He said it is intended to ensure all votes are treated equally. He said the GOP parties want consistency among all counties when handling the mismatched-signature verification process.

"Our intent was never to suppress," Johnson said. "Our intent was to ensure all counties to follow the law. Because of what Maricopa and Pima have done, it is essential that all counties get the same benefits."

Democratic attorney Marc Elias on Twitter said Democrats are asking to intervene in the lawsuit "to protect those votes and ensure a fair count."

"We did not misconstrue anything," he said via Twitter. "The GOP has been trying to disenfranchise voters and prevent lawful ballots from being counted."

Democratic leaders challenge lawsuit

"Bring it," Fontes, a Democrat who oversees the county's election process, tweeted in response to the lawsuit.

Sinema's campaign manager Andrew Piatt said in a statement that the public "must have faith that their votes are counted, and we are working diligently to ensure that count proceeds in a fair, transparent, and timely manner that voters can trust."

Felecia Rotellini, chairwoman of the Arizona Democratic Party, promised a fight if votes are discounted.

"The Republican party is doing everything it can to silence thousands of Arizonans who already cast their ballots," she said in a prepared statement. "That's absolutely wrong, and the Arizona Democratic Party is fully prepared to fight to ensure that every last Arizonan has their vote counted."

MORE: These key Arizona elections are still undecided

Andy Gordon, an election-law attorney who represents Democrats, said the lawsuit is without merit. The arguments contained in the lawsuit were characterized to him by a person familiar with it, he said.

"It's classic Republican eleventh-hour stuff," he said. "There are counties all over the state who have been doing this forever … and so now that we’ve got a different regime down here in Maricopa County, and we’ve got a really, really, really tight Senate race. Suddenly, the Republicans say, 'You shouldn’t’ be doing this, we need to call it off.'"

Gordon noted that aggrieved parties are required to act if issues arise: "You can’t sit on your hands until we see 'OK, now it’s close now we want to do something about it' "

Republicans defend the lawsuit

Chris Herring, the Maricopa County Republicans chairman, said it was his understanding that several county recorders were “treating ballots differently” when it came to verifying signatures.

“We just want all 15 counties treated the same way," he said.

Arizona Republican Party Chairman Jonathan Lines, on behalf of the Arizona Republican Party, appeared to lay the groundwork for a legal complaint Sunday.

He sent all county recorders a letter calling into question the extended curing process and separate emergency-voting processes in which some counties allowed voters to cast ballots over the weekend and on Monday.

No lawsuits have been filed over emergency voting.

This is the first year Maricopa County has offered emergency voting, but other counties have offered the extra polling hours for years.

In his letter, Lines argued that state law does not allow recorders to offer early voting after the Friday before Election Day except in specifically defined emergencies. It asked the counties to "identify and segregate all ballots" cast at emergency vote centers.

Fontes confirmed Thursday that the approximately 3,000 ballots cast at Maricopa County emergency vote centers "are going through the normal process at this time."

"They will be counted. I don't have a court order or anything else telling me to do otherwise," he said.

Democrats also file lawsuit

The Arizona Democratic Party late Thursday filed a separate lawsuit against Fontes. Its legal challenge also focused on ballots that needed signature verification — but with a different end goal in mind.

The lawsuit alleges Fontes did not promptly comply with the party's public records request for a list of voters whose ballots were not counted due to mismatched signatures, out-of-precinct votes or because poll workers were unable to verify a voter's identity or residency at the polls.

The party wants that information so it can "notify and assist eligible Arizonans in curing any defects in their ballots before the deadline," which is Nov. 14. The legal complaint mentions the Sinema-McSally toss-up as the chief reason for the party's concern.

The Democratic Party is asking a Maricopa County Superior Court judge to compel Fontes to immediately release the records. Mohave and Pima counties have already provided similar records to the party, according to the complaint.

Fontes did not immediately respond to a request to comment on the lawsuit.

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