The day after Ohio postponed its primary elections due to concerns about spreading the coronavirus -- and despite a recommendation from Gov. Mike DeWine, a Republican, that the state hold its election on June 2 -- there is still not a clear plan for when or how Ohio voters will cast their ballots in their primary elections.

Amid growing fears of the spread of the coronavirus, and warnings from the Centers for Disease Control and Prevention against large gatherings, DeWine filed a suit Monday in a lower court to get the state's primary elections postponed. The court ruled against him, and DeWine decided that he would keep the polls closed anyway, ordering state Director of Health Dr. Amy Action to use broad powers given to her under Ohio law to prevent the spread of disease to order the election be stopped.

"During this time when we face an unprecedented public health crisis, to conduct an election tomorrow would force poll workers and voters to place themselves at an unacceptable health risk of contracting coronavirus," DeWine said when announcing the decision.

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The Ohio Supreme Court then early Tuesday morning refused to grant an 11th-hour request to force DeWine to hold the election, giving at least a tacit legal endorsement of the governor's move.

But unlike other states, an election day can only be set by the state legislature or a court in Ohio. Because of that, when DeWine declared that he would not allow polls to open Tuesday for public health reasons, neither he nor anybody in his administration had the authority to actually change the election to a new date as has happened in other states.

So, as of Wednesday morning, Ohio voters have not yet had their say in who will be the Democratic nominee for president or in primaries for a variety of other offices, and they don't have any set alternative to cast their ballots. There also appears to be no consensus idea for how or when to hold the primaries.

DeWine and Ohio Secretary of State Frank LaRose indicated that they wanted to move the primary to June 2, and LaRose essentially declared it so in a directive issued Monday. "On Tuesday, June 2, 2020, boards of elections must conduct in-person voting at polling locations in their county," the directive reads. That directive is linked to voter information web pages including the Cuyahoga County Board of Elections and the Ohio Democratic County Chairs Association.

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That directive from the Republican LaRose drew harsh criticism from House Minority Leader, Democrat Emilia Sykes, for what she said was "sharing inaccurate information during a time of chaos when Ohioans are turning to him for truth and guidance."

"As the state's chief election officer, Secretary LaRose is uniquely charged with the proper execution of a fair election in the state of Ohio. That includes sharing accurate information. What has transpired in recent hours has been anything but," Sykes said in a Tuesday statement.

"Now in the hours following the chaos, he continues to send out press releases and share information on his website saying the election day has been moved to June 2nd. That is just wrong. As the governor has noted, and state law requires, only the legislature or the court has the power to set or change the election date and thus far, neither entity has done that. Yet LaRose continues to suggest people can continue to vote absentee in direct violation of state law. This too is wrong."

The state's Democratic Pary chairman, David Pepper, has said that he does not think a June 2 election is sufficient and also made clear that neither DeWine nor LaRose can unilaterally set a new election day.

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"Unfortunately, the proposed June 2 in-person primary arguably lacked legal authority but also brought with it major problems," Pepper said in a statement on Facebook Tuesday night. "The lateness of it is highly problematic for a host of reasons, including missing deadlines to send delegates to nominating conventions. And it is iffy to think this virus crisis will be resolved by then to even have in-person voting."

Pepper did, however, indicate that DeWine was open to working on multiple possibilities, saying the governor had indicated "that there was no 'magic' to his June 2 proposal."

In a statement on behalf of the state Democratic Party, Pepper said it had filed a suit with the Ohio Supreme Court to ensure that no legal technicalities ended up preventing Ohio voters from getting their chance to cast a ballot.

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"Earlier today we said that we would litigate to defend voters’ right to fully participate in the state’s Democratic primary election, and in the absence of action by the General Assembly and with other actors moving to shut down the primary, we have filed with the Ohio Supreme Court to ensure that all eligible Ohio voters are able to exercise their right to vote in this primary," Pepper said. "Yesterday’s actions did not create unchecked authority with the governor or secretary of state to run a new election. So authority for a new election must come from the legislature or from a court."

On ways to potentially hold an election, Pepper said on Fox News Tuesday afternoon that he would prefer extended vote-by-mail and potentially a curbside drop-off voting option.

Apparently understanding that they would have to go through further steps in either the legislature or the courts, DeWine and LaRose issued a joint statement Tuesday scaling back the "must[s]" used in LaRose's Monday night directive to strong suggestions for how Ohioans should be able to vote in their primaries.

"Last night, the actions taken by Ohio Department of Health Director Dr. Amy Acton saved Ohio lives," the statement read. "By preventing Ohioans from going to polling locations, we averted a situation which would have gone against the most recent scientific evidence available and could have dangerously advanced the spread of coronavirus across Ohio."

It continued: "As we move forward, it is vitally important that Ohioans have a significant period of time to cast mail-in absentee ballots and an opportunity to vote in-person, as was provided in the directive issued last night by the Secretary of State."

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On the legislative side of things, Republican Senate President Larry Obhof issued a statement Tuesday afternoon saying he would work with LaRose and DeWine to find a legislative solution to Ohio's election confusion.

"We recognize the difficult position the state is in and the need to protect public health, while maintaining citizens' access to all of their rights, including the right to vote," Obhof said. "The Senate will work collaboratively with the Governor and the Secretary of State in the coming days on any legislation necessary to deal with this unique and challenging set of circumstances, including determining a new date for the primary election... I believe that it is important for the Governor, Secretary of State, and legislature to work together in this time of crisis."

State Senate Minority Leader Kenny Yuko, a Democrat, also said that he thinks the legislature should be the body that addresses how a new election should be held.

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"The legislature has to quickly address the confusion caused by moving the primary election on such short notice," he said in a statement. "The fate of many community levies and local issues hangs in the balance and wrapping up the primary before June 2 should still be on the table... Our caucus will be putting forward our ideas on how to address this, and other critical issues facing Ohioans, before our next session day."

By the time Ohio straightens out its election situation, however, it appears unlikely its votes will matter in the presidential primaries. President Trump clinched the GOP nomination for president Tuesday and former Vice President Joe Biden expanded his delegate lead over Vermont Sen. Bernie Sanders with wins in the three states that did hold elections Tuesday -- Arizona, Florida and Illinois.

But Yuko is correct that Ohioans will still have other local races and issues to decide once it figures out how it will hold its postponed elections, whenever and however that is.