“A litigant who loses in a federal court of appeals, or in the highest court of a state, may file a petition for a “writ of certiorari,” which is a document asking the Supreme Court to review the case. The Supreme Court, however, does not have to grant review. The Court typically will agree to hear a case only when it involves an unusually important legal principle, or when two or more federal appellate courts have interpreted a law differently. There are also a small number of special circumstances in which the Supreme Court is required by law to hear an appeal.”
Respect has nothing to do with it. The federal supreme court has no jurisdiction over New York State criminal cases.
I am not a lawyer, but this site states:
“A litigant who loses in a federal court of appeals, or in the highest court of a state, may file a petition for a “writ of certiorari,” which is a document asking the Supreme Court to review the case. The Supreme Court, however, does not have to grant review. The Court typically will agree to hear a case only when it involves an unusually important legal principle, or when two or more federal appellate courts have interpreted a law differently. There are also a small number of special circumstances in which the Supreme Court is required by law to hear an appeal.”