The justices split 4-4 on the case, which means a lower court ruling siding with former Viacom executive Tom Freston remains in place.
Lower courts had sided with Freston against New York City's board of education, saying the city must pay for educating the learning-disabled student, even though he had been enrolled in private school.
The student's parents had insisted that public schools were unable to meet the child's needs. His learning disabilities were diagnosed after he was enrolled in private school.
The board of education had asked the justices to take the case after a lower court said tuition reimbursement is available to the parents under the Individuals With Disabilities Act.
The Supreme Court voted 4-4, with Justice Anthony Kennedy not participating in the case. The justices announced their vote in a two-sentence statement. No explanation was given for Kennedy's absence from the case.
The New York City board of education had asked the justices to take the case after a lower court said that tuition reimbursement is available to the parents under the Individuals With Disabilities Act.
Lawyers for the boy's parents said the special education program proposed by the public school system was inadequate to meet the child's needs.
The parents say that under federal law, they may challenge inappropriate proposals and obtain reimbursement for the costs of placement in private school.
In arguments before the Supreme Court on Oct. 1, New York City's top appeals lawyer argued that when a school district says it has a good program for special ed students, the law requires parents to enroll their children in the program before transferring to private school and seeking reimbursement.
The nation's main special education law guarantees every student a free appropriate public education and requires school systems to pay for private placements when their own programs or classrooms are not suitable.
Nationwide, the number of special education students placed in private schools at public expense has risen steadily, from about 52,012 pupils in 1996 to 71,082 in 2005, according to the U.S. Department of Education. Overall, however, the number of such placements remains relatively small - just 1.1 percent of the country's 6.1 million special education students.
In New York, a growing number of parents have been exploring a private-school option. During the 2002-2003 school year, the city received 3,908 tuition reimbursement requests, officials said. By the 2005-2006 school year, that number had jumped to 4,804.