Chancellor Carmen Fariña implied Thursday that some city charter schools prop up their state test scores by encouraging students to enroll elsewhere late in the school year.

“There shouldn’t be a whole movement out of charters the month before the test,” Fariña told reporters on Thursday morning. The well-timed attrition is not happening at all schools, she said, adding, “It happens in some places.”

Though she has expressed concerns about charter schools in the past, Fariña’s comments were perhaps the most provocative she has lobbed at the charter sector since taking over the school system. Her comments echo longstanding critiques of charter schools — which serve a smaller percentage of students with disabilities and English language learners than district schools do, and aren’t required to take new students mid-year — though higher-than-average student attrition from charter schools hasn’t been borne out by recent research.

[Update: Charter Center CEO says Fariña has ‘obligation’ to release enrollment data after push-out claims]

Fariña made the comments after speaking to Partnership for New York City President and CEO Kathryn Wylde at a conference on Thursday. In her conversation with Wylde, Fariña ticked off ways she supports charter schools, including school visits, inviting them into her Learning Partners Program, and inviting them to the city’s professional development sessions.

“Where we need to do more work is better transparency,” Fariña said.

Asked to elaborate after the talk, she said she was concerned that charter schools look to replace students who leave with only students with top test scores.

She said she wants “to ensure that, as there are openings in upper grades, that the kids that are accepted in are not just kids who get postcards because they’re level 3s or 4s to come to the school.”

Fariña doesn’t oversee most of the city’s charter schools, which are independent from the Department of Education and enroll students through lotteries. But she serves on the board of the New York City Charter School Center and, as the city’s top education official, her public statements on the issue are closely monitored.

Fariña isn’t the only high-ranking education leader to say that more attention should be paid to charter schools’ enrollment practices. Last year, Board of Regents Chancellor Merryl Tisch urged state education officials to create a “stability index” that would flag suspicious trends like high student discharge rates right before state testing. (A spokesman for the State Education Department could not immediately say whether that metric had been developed.) Earlier this month, Tisch agreed with Fariña’s calls for more transparency on a panel with State Education Commissioner John King.

When students leave charter schools in the middle of the year, many end up in district schools, which can put a new burden on the school charged with getting the student adjusted. Whether charter schools lose students at a higher rate than district schools has been the subject of a number of recent analyses.

A 2012 SchoolBook analysis looked at three years’ worth of student discharge data and found that average student mobility rates were lower for charter schools than they were for traditional public schools, though turnover was higher in some charter-heavy districts. Last year, the Independent Budget Office looked at attrition in lower grades for all city schools and released similar findings.

Another study, released in 2013 by the Center on Reinventing Public Education, looked at 25 charter elementary schools and concluded that the special-ed gap was caused by parents’ enrollment choices, not students being pushed out.

None of those studies looked at when during the year students exited a school.

If Fariña is serious about probing charter schools’ enrollment data more deeply, she could make it happen as the city schools chancellor, said Ray Domanico, the director of education research at the IBO. The department tracks student discharges from district and charter schools by date, he said.

The debate over charter schools will be amplified in the coming months with the state legislature expected to consider lifting a cap on the number of schools allowed to open in the city. As in 2010, when the cap was last lifted, the conversation is likely to include calls for schools to enroll more high-needs students.

On Thursday, Fariña said she wants to see more attention on those issues.

“We need to make sure that, when you say that these are the kids that are enrolled through the lottery,” Fariña said, “that these are the kids you graduate.”