One of the most exclusive schools on the Upper West Side could be included in a controversial integration plan after all — just a year later.

The apparent reversal regarding the Center School came after the New York Post reported that the school was left out of the proposal being debated in District 3. Under the plan, a quarter of seats at every middle school in the district would be reserved for students who struggle on state tests.

The Center School has become known for enrolling the children of celebrities such as “Sex in the City” star and gubernatorial candidate Cynthia Nixon, who once argued against a proposal to move the school because she worried it would exacerbate segregation. The Center School serves among the fewest poor students in the district, and last year was almost 60 percent white — almost double the district average.

Yet the Post reported on Sunday that the school was exempt from the integration proposal because it enrolls students starting in fifth grade, instead of sixth. The tabloid also raised questions about how students are admitted there, calling the application process “a mystery.” The school is one of the few citywide that still runs its own admissions, instead of being overseen by the education department.

“They have their completely own, independent rubric which they don’t have to release or justify,” Alina Adams, an education consultant, told the Post. “Nobody knows how kids get into that school.”

The report prompted questions from elected officials. City Councilman Ritchie Torres asked the Department of Investigation and the Human Rights Commission to look into the school’s admissions and why it wasn’t included in the integration plan, the Post reported Monday. And City Councilman Mark Treyger, who heads the education committee, wrote a letter to the chancellor demanding similar answers.

“We need to ensure that all students have the same education opportunities, and that starts by making sure that our schools have transparent application processes,” Treyger wrote.

Many integration advocates have made similar arguments. Critics of the city’s screening process — which allows some schools to pick their students based on factors such as report card grades and attendance — say the system is often confusing and favors parents who have the time and savvy to figure it out.

Since test scores are closely linked to race and class, the District 3 proposal could integrate schools on multiple levels. But it has faced pushback from parents who have come to expect that high test scores — achieved most often by the district’s middle-class students — should guarantee families their top choice of middle schools. No changes have been formalized yet, but the district superintendent hopes to have a plan in place for the 2019-20 school year.

Should it take effect, education department spokesman Doug Cohen said it would apply to Center School fifth graders entering in the 2020-21 school year. He added that the department is “working” to bring all middle schools under its centralized process for the next admissions cycle. That includes Center School.

“As part of the transition, the school will begin posting its admissions rubric,” Cohen wrote in an email.