The case you're referring to is Dred Scott v. Sanford, widely held to be one of the most infamous rulings in the history of SCOTUS.

To give background, African Americans were already of contentious legal status, depending on where they lived and whether they were enslaved or free. Slaves obviously had no real rights, but free blacks in some states could vote and hold property (James McPherson, Battle Cry of Freedom, p. 174). The chief justice of the court, Roger B. Taney, was determined to use the case as a battering ram against free blacks. He was, to put it bluntly, a Southern partisan and a diehard white supremacist, even by the standards of his time. As James McPherson writes,

"Taney’s opinion took up first the question whether Dred Scott, as a black man, was a citizen with the right to sue in federal courts. Taney devoted more space to this matter than to anything else. Why he did so is puzzling, for in the public mind this was the least important issue in the case. But southern whites viewed free blacks as an anomaly and a threat to the stability of slavery; Taney’s own state of Maryland contained the largest free Negro population of any state. The chief justice’s apparent purpose in negating U.S. citizenship for blacks, wrote Fehrenbacher, was “to launch a sweeping counterattack on the antislavery movement and . . . to meet every threat to southern stability by separating the Negro race absolutely from the federal Constitution and all the rights that it bestowed.” To do so, however, he had to juggle history, law, and logic in “a gross perversion of the facts.” Negroes had not been part of the “sovereign people” who made the Constitution, Taney ruled; they were not included in the “all men” whom the Declaration of Independence proclaimed “created equal.” After all, the author of that Declaration and many of the signers owned slaves, and for them to have regarded members of the enslaved race as potential citizens would have been “utterly and flagrantly inconsistent with the principles they asserted.” For that matter, wrote Taney, at the time the Constitution was adopted Negroes “had for more than a century before been regarded as beings of an inferior order . . . so far inferior, that they had no rights which a white man was bound to respect.” (McPherson, Battle Cry of Freedom, p. 174)

The decision was met with outrage and hostility by many Northern states, and their legislatures passed resolutions that basically said 'we don't care what SCOTUS says,' so enforcement of the ruling largely depended on where you lived. Thankfully, the ruling didn't stand for very long. It was nullified by the ratification of the 14th Amendment in 1868, which guarantees citizenship to all people born on U.S. soil.