When D.C. families choose a school that is not their assigned neighborhood campus, they tend to select schools that educate fewer students from low-income families, according to an 86-page study released Thursday from the Office of the D.C. Auditor.

The result: Traditional neighborhood public schools, particularly in low-income neighborhoods, struggle with declining enrollment over the long term and have higher concentrations of students living in poverty. Smaller schools are more expensive to operate, leaving campuses with less money to hire staff.

The plight of those schools is also complicated in the middle of the school year when students transfer from other campuses and school systems, arriving after per-pupil funding has been allocated. That causes schools to be even more cash-strapped.

The study — conducted in partnership with the Johns Hopkins School of Education Center for Research and Reform in Education — marks the auditor’s most comprehensive examination of enrollment and transfer patterns among the District’s nearly 100,000 public school students.

Kathy Patterson, the D.C. auditor, said the findings illustrate the unintended consequences of having a city with many school options for families.

Every student has an assigned neighborhood school — but that doesn’t mean children attend that campus. A citywide school lottery placement system aims to make it easier for families to apply to traditional public and charter campuses other than their designated schools.

Four in 10 public school students in the District attend their assigned neighborhood school or a campus — often a charter school — closer than their assigned schools.

About 47 percent of students in the District attend charter schools, which are publicly funded but privately operated.

“One of the big takeaways is that we don’t quite understand all of the effects of the very robust choice environment we have created here,” Patterson said. “And that’s something we absolutely want to know more about.”

The auditor’s office recommended the city examine why families perceive schools with high concentrations of at-risk children as lower-quality campuses.

For example, only 9.8 percent of students who live in the boundaries of Anacostia High — a neighborhood school in Southeast Washington — have elected to attend the school. It has an at-risk population of 81 percent, and 35 percent of students require special education, according to city data.

By comparison, Thurgood Marshall Academy — a charter high school near Anacostia High — has an at-risk population of 54 percent. Twenty percent of its students have special education needs.

“Future research could explore to what extent schools with larger at-risk populations suffer from a lack of investment or are further disadvantaged in D.C.’s current school choice system,” the study says, “and how policy levers could be used to help ensure a high-quality education for all students in the District.”

The bulk of the study explores the effect that these enrollment patterns have on school funding.

Campus budgets are based on enrollment, and the auditor sought to determine whether the city is accurately predicting enrollment for individual schools. Students with special education needs and those considered at-risk — which means they are homeless, in foster care or their families qualify for public assistance — receive extra funding.

These students transfer schools more frequently than students citywide on average each year, according to the study. That can make it trickier to predict which schools they attend each year.

The auditor’s office found that the District is accurate in projecting citywide enrollment, but estimates are less accurate for individual schools. The city may accurately predict that 11 percent of students are learning English as a second language, but they may be off in determining which schools those students will attend.

Estimates for individual campuses are often off by more than 5 percent, the study found.

But Deputy Mayor for Education Paul Kihn said that the city’s enrollment projections are accurate and that the District accounts for midyear transfers with budgets for schools.

He said his office has commissioned a study to determine whether it is allocating funding for at-risk students in an effective way.

“Accurate budgeting also ensures that the city does not have to face a budget shortfall: If the projections are too low, the District must find contingency funds after the budget has already been approved and committed,” Kihn said in a letter responding to the auditor’s study. “We look forward to working with our schools, school communities, and agencies to continue to improve upon our processes and help plan for the future.”

During the school year, traditional campuses receive more transfer students than charters do.

The city conducts an official count of students in October, which determines a school’s funding. Nearly all charter schools experienced a decline in students after the October count, the auditor’s study said. In contrast, most neighborhood schools gained students, and neighborhood schools with the highest percentages of at-risk students gained more.

According to the auditor’s office, 18 percent of students attending campuses in Wards 7 and 8 — the swaths of the city with the highest concentrations of poverty — changed school from one year to the next. That eclipses the citywide average and does not include students who switch schools because they are starting middle or high school.

Patterson and Erin Roth, director of education research at the auditor’s office, said they hope the D.C. Council uses the study to examine whether city policies perpetuate student transfers. They said academic outcomes suffer when students frequently transfer schools.

“All school choice, be it residential or a lottery, privileges those with the most capacity and access,” Roth said. “If the intent is to break down those barriers, then perhaps we need to build in parameters to facilitate this in the lottery.”