28 USCS § 1258 provides that final judgments or decrees rendered by the highest court of a State in which a decision could be had, may be reviewed by the Supreme Court by writ of certiorari where:

• the validity of a treaty or statute of the United States is drawn in question; or
• the validity of a statute of any State is drawn in question on the ground of its being repugnant to the Constitution, treaties, or laws of the United States; or
• any title, right, privilege, or immunity is specially set up or claimed under the Constitution or the treaties or statutes of, or
• any commission held or authority exercised under, the United States.

Upon writ of error, the Supreme Court has no jurisdiction to review a judgment of a state court, unless it is a final judgment, by the highest court of the State in which a decision in the suit can be had, and against a right set up under the Constitution or laws of the United States, pursuant to Rev. Stat, § 709 (United States).[i]

[i] Great Western Tel. Co. v. Burnham, 162 U.S. 339 (U.S. 1896)