In a sweeping national “mystery shopper” experiment, researchers posing as parents sent emails to thousands of schools asking how to apply for admission.

Some messages said their child had a disability. Others said their child sometimes had trouble behaving in class, or struggled with academics.

The results: charter schools and certain traditional district schools were more likely to ignore parents who indicate their children may be tough to educate, and charter schools in particular are more likely to ignore inquiries that appear to be from families of students with disabilities.

It’s powerful new evidence that schools can exert real influence over who ends up in their classrooms — and offers one explanation for why charter schools nationally serve a smaller share of students with disabilities than traditional public schools.

“For schools of choice, charter and the traditional publics behave fairly similarly, with the exception of special needs kids,” said Peter Bergman of Teachers College, who conducted the study with Isaac McFarlin of the University of Florida. “It’s certainly disconcerting.”

The researchers sent the emails to nearly 6,500 schools in 29 states and Washington, D.C. Many had basic messages like, “I am searching for schools for my daughter. Can anyone apply to your school? If so, can you tell me how to apply?”

Other emails implied that the student had a significant disability. “Her IEP says she has to be taught in a separate room,” the messages said, referring to individualized education programs describing the resources or services a student needs. The emails also used a variety of names, including ones commonly associated with Hispanic and black families.

When the emails included no additional details, schools responded 53 percent of the time. But schools overall were 7 percentage points less likely to respond to messages referencing behavior problems, 5 percentage points less likely to respond to messages mentioning a significant disability, and 2 percentage points less likely to respond to Hispanic-sounding names.

Charter schools in particular were less likely to respond to the messages mentioning a disability than to the standard messages — 7 percentage points less likely. Schools the researchers identified as “no excuses” charters were 10 percent less likely to respond to emails mentioning the disability.

“It reflects what we know anecdotally,” said Lauren Rhim, the executive director of the National Center for Special Education in Charter Schools. “Parents of students with disabilities aren’t able to access choice in the same way others are.”

The findings are notable because research on charter schools and students with disabilities tends to focus on how enrollment numbers compare to the surrounding district, or whether students end up leaving a school once enrolled. This research looks at what can happen before any of that, opening up a part of the admissions process that can be most opaque: interactions between prospective parents and schools.

“A lot of charters may argue, we don’t counsel anyone out,” Bergman said. “We’re taking one giant step backwards and saying, hey, we want to look at what happens before families apply. We think those interactions can be very important.”

Others think so, too. The D.C. Public Charter School Board, which authorizes charter schools in Washington, D.C., has its own mystery-shopper program where it calls schools to see how they respond to admissions questions. The Massachusetts state education department has also tried it.

Charter advocates said the study didn’t show that students were kept from enrolling at the schools, but acknowledged communication with prospective families could be improved.

“We did not see in the study any findings that students were in fact prevented from enrolling in any charter school for any of the reasons that the researchers were testing,” the National Alliance for Public Charter Schools said in a statement. “The study does however suggest that schools could improve their administrative and communications practices when responding to inquiries from members of the public and parents.”

The new study also offers evidence that charter schools’ reluctance to respond to messages indicating a student has a disability may be tied to the way they receive funding.

In states where schools are reimbursed for most of what they actually spend on special education, like Michigan and Wisconsin, schools were no less likely to respond to those messages, the researchers found.

“It’s very unusual to have a study that has such a clear implication for policy to solve a problem,” said Brian Gill, a senior fellow at Mathematica Policy Research, though he noted that funding method could have other downsides.

McFarlin said he hopes the findings can prompt discussion among both district and charter schools. Both, he said, are discouraging some parents through their actions.

“We think these are issues that can be addressed,” McFarlin said. “That’s the hope for what comes out of this.”

Francisco Vara-Orta contributed reporting.