Voters across the state have been slow to return their mail ballots, which could translate into a historic bottleneck at the polls Tuesday as Californians wait until the last minute to cast their ballots in the Democratic presidential primary.

The return rate is especially bad among the state’s millions of no-party-preference voters, many of whom are apparently confused about what they need to do to cast a ballot in the Democratic primary.

Only about 12% of the 4.1 million vote-by-mail independents have returned their ballots and fewer than 1 in 10 requested the “crossover” Democratic ballot, said Paul Mitchell of the nonpartisan Political Data Inc., which provides information on voting and ballots to campaigns across the state.

As many as 40% of no-party-preference voters who returned their mail ballots early didn’t vote in the Democratic presidential primary, many because they didn’t know how to get that ballot, he added.

But changes in the way much of California votes, along with a hard-fought Democratic presidential primary, affect all voters in the state, not just independents.

A new election system that automatically sent mail ballots to more than three-quarters of the state’s voters, and the prospect of Democratic voters still undecided about whom to support, are getting the blame for the delay.

More than 16 million ballots were mailed to voters earlier this month, but as of Friday morning, only about 2.9 million, or 18%, had been returned. It was 26% in 2016. With 20.4 million registered voters, that leaves election officials looking at a flood of ballots that could land Tuesday.

“It’s going to be a very busy election day,” said John Arntz, San Francisco’s elections director.

That won’t make it any easier for California to get its results out. Mail ballots dropped off at the polls on election day aren’t counted immediately, and any votes that arrive in the mail by the Friday after the election are included in the tally.

The result is a vote count that can take days or even weeks to complete.

For a number of counties, including big ones like Los Angeles and Orange, this will be their first election under the state’s Voter’s Choice Act, a system in which voters automatically receive their ballots in the mail.

That change apparently is causing some problems, said Mitchell.

“Voters who are getting a mail ballot for the first time have been slow to return them,” he said. “Most people have a type of internal clock about when they vote, and it’s hard to change that.”

But a look at the voters who aren’t returning their ballots also suggests it’s no accident that the mail ballots are slow to arrive, Mitchell added.

“It appears that older Democratic voters, who are typically highly likely to vote, are holding on to their ballots,” he said.

While Vermont Sen. Bernie Sanders is leading the polls in California and the nation, there are seven other high-profile Democrats on Tuesday’s presidential ballot. With the South Carolina primary on Saturday, California voters who are not enthusiastic about Sanders may want to see who comes out on top there before making their choices.

Plenty of pundits have been advising voters to hold off on returning their ballots until election day. Californians who made their choices as soon as their ballots landed in the first week of February may have found themselves voting for businessman Andrew Yang, who dropped out of the race on Feb. 11.

“In 2016, it was a binary choice for Democrats; they didn’t have to think past Sanders or (Hillary) Clinton,” Mitchell said. “But now it’s harder.”

The complicated rules about just who can vote in what primary also could result in lines at the polling places.

Only registered Republicans are allowed to cast ballots in the GOP primary. But the Democratic primary is open to voters who aren’t members of another political party.

There’s a hitch, however: Those independents have to ask for that Democratic ballot.

Despite emails and postcards to voters from Secretary of State Alex Padilla and county registrars across the state warning of those rules, fewer than 10% of independent voters requested Democratic mail ballots.

A study by Mitchell and Capitol Weekly found that two-thirds of all independents and more than 80% of those most likely to cast ballots wanted to vote in the Democratic primary. But many of them didn’t know how to get that ballot or even if they were eligible to vote for the Democratic candidates, Mitchell said.

“The burden is on the voter,” he added.

Although the deadline has passed for receiving a mail ballot, independent voters can still get a Democratic ballot by showing up at a polling place and asking for one. But that means more people crowding into the polls and taking more time to get the right ballot, slowing the voting process.

In San Francisco, “a lot of the early voting is by people requesting a crossover ballot,” said Arntz, the city elections chief. In Los Angeles, reports indicate as many as half of the people showing up at voting centers are independents looking for Democratic ballots.

The turnout for California’s 2018 midterm elections was the highest in decades for a nonpresidential election, and there’s no sign voters’ enthusiasm has diminished. The slow early-vote returns may just be a glitch or an aberration ahead of an election day flood.

“At this point, it appears the turnout is slower than expected,” said Mark Church, San Mateo County’s registrar. “However, what we have experienced in previous (all-mail ballot) elections is a huge influx of returned ballots ... starting on the last Friday before the election.”

But the state is venturing into unknown territory with this election. The new, earlier primary date, the increase in counties that vote by mail, the growing number of independent voters and the presence of a hot, state presidential primary race on the Saturday before Californians cast their ballots can all affect turnout.

“There are so many moving pieces, it makes reading the tea leaves really hazardous,” Mitchell said.

John Wildermuth is a San Francisco Chronicle staff writer. Email: jwildermuth@sfchronicle.com Twitter: @jfwildermuth