Nassau’s top Republicans and Democrats agree: Tuesday’s presidential primary is almost certain to drive higher turnout to the closely watched special election to replace former state Sen. Dean Skelos.

But nervous party leaders say it’s impossible to predict the primary’s precise impact on the Senate vote — the so-called “down-ballot effect” — because of the unique and complicated way the two elections will be administered.

For one, they won’t actually be on the same ballot.

Any of the 232,650 people registered to vote in the 9th Senate District, which covers southwestern Nassau, can participate in the special election. But only the district’s 75,614 registered Republicans and 94,639 Democrats can vote in their respective primaries, and those who wish to choose candidates for both president and state senator have to do so individually by going to separate tables at their polling place.

Will many South Shore primary participants — including new and infrequent voters coming out for populist candidates Donald Trump and Bernie Sanders — not bother with the special election?

Will some be confused, despite the county Board of Elections’ effort to clearly label the different lines?

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Officials with an interest in the Senate race between Republican Christopher McGrath and Democrat Todd Kaminsky just don’t know.

“You’re like the pilot that’s flying blind,” said Nassau Democratic chairman Jay Jacobs. “If you don’t have a pit in your stomach, you’re not alive.”

“This is going to be interesting,” said Nassau GOP chairman Joseph Mondello. “The question is going to be: do they get in the second line? That’s the unknown.”

The stakes are high. The McGrath-Kaminsky race has been among the most expensive in recent State Senate history, with the candidates spending roughly $850,000 each in under three months, as of April 4, and an anti-Kaminsky Super PAC last week buying $1.2 million in television ads.

Kaminsky, a state Assemblyman from Long Beach, and McGrath, a personal injury attorney from Hewlett, are vying to succeed Skelos (R-Rockville Centre), the former senate majority leader convicted last year of federal corruption crimes. Laurence Hirsh, an accountant from Valley Stream, is running on the Green Party line.

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The winner of the race could help determine control of the Senate, as Republicans now hold a slim majority aided by a group of breakaway Democrats.

Typically, a special election to decide a local seat brings out mostly die-hard party loyalists. In recent years, standalone contests to fill county legislative seats netted turnouts between 4 and 11 percent.

“They’re usually tests of the pull of the two organizations,” Mondello said, referring to each party’s stable of executive leaders and committeemen.

The county’s last special election to fill a State Senate seat, in Feb. 2007, had a 27 percent turnout, doubling officials’ expectations.

Mondello said he expected something similar on April 19. Jacobs predicted something far exceeding the recent county legislature special elections.

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Democrats, though, view the potential gap between presidential and State Senate voters as serious enough to have former President Bill Clinton mention it while he was rallying supporters for Hillary Clinton in Elmont this month.

“We’ve got a chance to get a bigger vote this time than we had eight years ago,” Bill Clinton said, referring to New York’s 2008 presidential primary, which was held in February, drawing 37 percent of Nassau’s registered Democrats and 20 percent of Republicans.

“But when you go to vote, you still have to go to a separate table to vote in the presidential primary as opposed to the local election,” Clinton told the crowd. “So I need to ask you to go out and make sure that everybody knows that.”

Tuesday’s presidential primary is expected to draw significant turnout statewide, largely because the candidates, with each party’s nominating contest still undecided, have campaigned extensively in New York.

Trump leads his Republican rivals, Texas Sen. Ted Cruz and Ohio Gov. John Kasich, by more than 30 percentage points in most statewide polls. Hillary Clinton, previously one of New York’s senators, leads Sanders, the Vermont senator, by about dozen points in recent polls.

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Nassau Board of Elections officials, expecting many new voters, say that polling places in the 9th Senate District will have clear signage labeling the tables for the different elections, as well as extra voting machines and personnel to aid voters.

But some advocacy groups say the election board should have contacted anyone eligible to vote in both the primary and special election to let them know that there will be two separate ballots that must be cast separately, in different parts of the polling place.

“Unfortunately, this has not happened. This is a serious injustice that will achieve nothing but suppress the vote,” several groups, including the New York Civil Liberties Union, wrote to the board in an April 11 letter.

Board commissioners did not respond to the advocates’ complaints.

The McGrath and Kaminsky campaigns, however, expressed confidence the elections will be properly handled.

“Turnout for both parties is going to be record setting,” said E. O’Brien Murray, a McGrath spokesman. “We have confidence the Nassau Board of Elections will be able to ensure the process is smooth.”

Evan Thies, a Kaminsky spokesman, said he believed the campaign would be able to capture many of the district’s 2,144 Democrats who since Jan. 1 have registered to vote for the first time, about double the number of newly registered Republicans in that time.

“All the data and energy point to a massive turnout for Todd Kaminsky,” Thies said.