By Jeremy Herb, Kelly Mena and Ellie Kaufman, CNN

(CNN) -- Remember hanging chads, Florida's 2000 election nightmare?

The 2020 equivalent could wind up being mismatched signatures.

With voting already underway in two states, Democrats and Republicans are drawing battle lines across the country over voter signatures for mail-in ballots, with lawsuits over how signatures are evaluated and whether voters can fix ballots that get tossed. President Donald Trump and Republicans are arguing for strict matches, while Democrats are pushing for easier rules letting people prove they are who they say they are, even if their John Hancocks have changed a bit.

Legal fights over absentee votes aren't a new phenomenon, but they've taken on a newfound importance because of the surge in requests for mail-in ballots and states expanding access to vote-by-mail and, in some cases, conducting elections almost entirely by mail for the first time.

The expanded mail-in voting has also led to more ballots being rejected -- with signature problems a key factor.

"You're much more likely to have your vote counted if you cast it in person. But for some people, that's not a safe option in November," said election law expert Rick Hasen, a professor at the University of California, Irvine and a CNN analyst.

"Ordinarily, if you're going to roll out mail-in balloting on a large scale, you do a big voter education effort," Hasen added. "But there's not really time for that or resources for that because of the pandemic."

Problems surrounding rejected mail-in ballots are especially concerning for Democrats, whose voters make up a sizable majority of those planning to vote by mail. In the most recent CNN poll, about half of former Vice President Joe Biden's supporters say they prefer to vote by mail. The poll found 68% of Trump's supporters said they prefer to vote in person on Election Day, as opposed to 21% of Biden supporters.

Democrats, including the party's House and Senate campaign arms, have invested millions this election cycle in legal efforts aimed at voting laws, including trying to make it easier for voters' ballots to be accepted and for those ballots to be "cured" if a ballot is rejected. Republicans, too, have put millions into fighting legal battles against Democrats.

Trump has continued to falsely claim mail-in voting is ripe with fraud, and last month he falsely said congressional Democrats were pushing legislation "banning signature verification," when the bill only includes a requirement for states to allow voters to correct signature problems. Trump harped on the matter again Saturday in an interview with Fox News' Jeanine Pirro.

"How about signatures? They don't even want to have signatures verified," Trump said.

During the primary season, hundreds of thousands of mail-in ballots were rejected across the country. Every state has different laws, but even innocent mistakes can invalidate a ballot: In New York, for instance, a ballot can be disqualified if it's sealed with a piece of tape. The Washington Post and NPR recently totaled data that showed the number was more than 500,000, though that didn't cover the whole country or account for ballots that voters fixed to allow them to count.

In Wisconsin, nearly 2% of mailed-in ballots were rejected in the April primary, according to the Wisconsin Election Commission -- meaning one out of every 50 ballots was tossed.

"If voters believe that there's a one in 50 chance their ballot would be rejected, they would be quite surprised," said Barry Burden, a professor and director of the Election Research Center at the University of Wisconsin-Madison.

Rejected ballots higher for minority voters

The issue is more widespread in the Black and Hispanic communities. One University of Florida study found Black and Hispanic voters in the state were twice as likely to have their ballots rejected as White voters. Younger voters were also more likely to have their ballots rejected than older voters, according to University of Florida professor Daniel Smith, who compiled the data from the Florida Division of Elections.

Those issues are already playing out in North Carolina, one of the two states where early voting has begun. While the numbers are very preliminary since early voting began on September 4, about 2% of the roughly 10,000 absentee ballots returned as of Friday had been rejected because of some issue, including potential signature problems, according to data from the state's board of elections.

That rejection rate was higher for Black voters, however, at nearly 7%. Voters in the state whose ballots are invalidated will be sent a new mail-in ballot.

"If you move, you may not even get your ballot, and we know younger voters, racial, ethnic minorities, lower-income voters tend to move more. That's certainly been the case with the pandemic. That's going to raise a problem with you getting your ballot in the first place," Smith said.

Florida, which has a long history of mail-in voting, had about a 1% rejection rate of vote-by-mail ballots in both the 2016 and 2018 general elections. Smith said ballots that are rejected generally fall into two categories: the ballot is received past the deadline or it has a problem with a signature in some form -- it's missing, it doesn't match or it's in the wrong place.

The signature verification process, which varies state-by-state, is one of the many steps that makes vote-by-mail highly secure. In 19 states, officials are required to notify voters of their signature discrepancy and give them an opportunity to fix or "cure" their absentee ballot in order to be counted, according to the National Conference of State Legislatures. That means that in more than half of the states, voters may never know their signature has been rejected. In 13 of the states with notification, voters are given some time after Election Day to fix the discrepancy.

Signature matching sparks legal battles

There have been legislative and legal fights in states without a ballot-curing process.

A federal judge ruled Tuesday in Texas, for instance, that the state must notify voters if a ballot has been marked for rejection due to a signature issue and give voters the opportunity to fix the problem.

Western District of Texas Judge Orlando Garcia found the state's process of rejecting ballots in the state was unconstitutional. The judge ordered Texas Secretary of State Ruth Hughes to either issue an advisory to local election officials saying that mail-in ballots may not be rejected due to a signature mismatch or an advisory instructing local election officials that they are required to take additional steps, such as notifying voters, before a ballot could be rejected due to a signature discrepancy.

"Before this, unless you called your local election officials on a daily or hourly basis to see if your vote had been recorded, there wasn't a way to know until after the election was completed and the numbers were sent to the state," said Celina Stewart, litigation director for the League of Women Voters, one of the plaintiffs in the case.

"This is significant because tens of thousands of ballots will be protected through this process," said Stewart, who argued that voters casting legitimate ballots were seeing them rejected.

Hughes' office did not respond to a request for comment.

A similar lawsuit was filed in North Carolina last week by local and national Democratic parties that argues the state's current process for addressing mail-in ballot errors is insufficient.

Democrats contend that small mistakes like missing a signature on an absentee ballot require a quick and efficient remedy. "This hurdle could leave North Carolinians who cast an absentee ballot but missed one line without a voice in this critical election. We must afford these voters the same rights we afford others who have made a similar mistake on the ballot," said state Democratic Party Chairman Wayne Goodwin in a statement on the lawsuit.

Other states have passed new laws this year to address potential problems.

In New Jersey, the state legislature passed a new law for curing rejected ballots in late August, following the state's decision to mail ballots to all registered voters for the first time in the 2020 election.

The new law requires local election officials to notify voters within 72 hours by email, mail or phone of their rejection, and it gives the voter up to five days after the polls close to fix their ballot.

Each state has its own quirks when it comes to mailing ballots and fixing problematic ones.

In Alabama, local election officials notify voters when their application for an absentee ballot has been disqualified, but it doesn't do the same for discrepancies on the absentee ballot itself due to election law that prevents mail-in ballots from being opened until after the close of polls on election night.

Grace Newcombe, press secretary for Alabama Secretary of State John Merrill, a Republican, told CNN that voters can still check on the state's website "to see if their ballot was rejected for some reason."