Final answer:
The court case that most likely overturned segregation in America was Brown v. Board of Education.
Step-by-step explanation:
The court case that most likely overturned the legal segregation of facilities in America was Brown v. Board of Education. In this landmark Supreme Court decision in 1954, the Court unanimously ruled that racial segregation in public education violated the Constitution. The decision overturned the previous precedent set by Plessy v. Ferguson in 1896, which had allowed for separate but equal facilities.