The Chicago Teachers Union has threatened to walk off the job on April 1 in a one-day strike, saying their employer unilaterally nixed their raises for education and experience.

Chicago Public Schools insists that any walkout, as the two sides continue bargaining, would be illegal. CPS has informed teachers who call off without a doctor’s note or written proof of an emergency that they will not be paid that day.

Despite the rhetoric, determining the legality of a strike at the end of next week isn’t up to either one.

That call and any consequences will be decided by the Illinois Educational Labor Relations Board, which is already overseeing a contract dispute between CPS and the CTU.

One of the sides, likely CPS, would have to ask the board to step in, said John Brosnan, a spokesman for the labor relations board.

“Almost everything has to come to us,” Brosnan said. “We don’t go out and enforce it. . . . Generally what happens is someone has to file a charge.”

The staff investigates and makes a decision, which can be appealed to the five-person board. Three of them were appointed by Gov. Bruce Rauner, who has tried to weaken labor unions.

Brosnan said he can’t recall the board ever dealing with a strike over unfair labor practices rather than stalled contract negotiations.

CPS will not commit to any reaction if its teachers skip work on April 1.

“We’re exploring all our options,” district spokeswoman Emily Bittner repeated late last week, adding that CPS could withhold up to $10 million in teacher pay.

The district argues any strike before mid-May is illegal because fact-finding hasn’t concluded, a pre-strike step required by state law.

After fact-finding in 2012, when CTU members walked out for seven days over a contract fight, CPS asked a Cook County judge to stop the strike. Negotiations resolved it before he ruled.

The CTU has already asked the Illinois labor relations board to rule on its “step and lane” raises, which CPS canceled in September. An initial vote sided unanimously with the district, but the matter still could have a full hearing.

The parties still haven’t agreed on a contract to replace the one that expired last June. In January, the Board of Education presented a “serious offer” to the union, as CTU President Karen Lewis described it. But the union’s 40-member bargaining team shot it down unanimously, saying the offer had too many loopholes.

Meanwhile, both sides have ramped up pressure. CPS threatened to take away a 7 percent pension contribution it has made on union members’ behalf, and announced three unpaid furlough days, including March 25. So the union hatched big plans to disrupt the district on April 1.

On Wednesday, the union’s 800-member House of Delegates will vote on recommendations to walk out that Friday and head downtown to snarl the Loop during the evening rush hour.

Once those actions are finalized, Bittner said the district will provide contingency plans for parents “on how we will keep students safe, fed and engaged.”

“CPS remains committed to working through the fact-finding process, and we will continue to bargain in good faith in the hopes that CTU leadership will join us in doing what is in the best interest of our children,” she said.

In a Facebook posting, CTU Vice President Jesse Sharkey asked concerned parents to “think of the ways that this could go if we have no new funding for the schools . . . come the fall, then a potential strike will be longer and more difficult — think weeks, not days.”

He said since schools can’t count on the mayor for more money. “We have to take matters into our own hands,” Sharkey said.