In a federal system there are usually two circumstances under which you may petition the supreme court. The first is if you have been denied relief in a federal court of appeals, and you want to appeal the decision, which is a matter of federal law. The second is if you have exhausted the appeals process through all courts of other jurisdiction, and want to assert that the decision rendered violates the country’s constitution or is otherwise not compliant with federal law in that nation. Parties who petition the supreme court rarely have the case heard, but those that do base the appeal on questions of law rather than questions of fact.
In determining whether or not you may successfully petition the supreme court in countries that operate with a federal system, you typically must first be sure that your case involves a federal matter as supreme courts generally only have jurisdiction over federal matters. In the US, the Supreme Court is a court of solely federal jurisdiction, so cases that have been decided according to state law will not be heard unless the argument is that state law is inconsistent with Federal law. For example, you may bring a case to the State Supreme Court arguing that a particular law violates both the State and Federal Constitutions. If the court rules against you on both grounds, then you may petition the Supreme Court of the United States with the argument that the law violates the Federal Constitution. They will not, however, hear cases that have been decided solely on state law.
Even when a case contains a question of federal law, one of the most common mistakes litigants make is to argue questions of fact that have been determined by the finder of fact at the trial court level. For instance, a party who petitions the supreme court on the basis that he or she did not actually commit an act that had already been determined to commit by the finder of fact in the trial court will have the petition quickly thrown out. If that same party argues that though he or she committed the act, prohibiting such action violates his or her rights under the country’s constitution, then there is a possibility that the petition will be granted.
In other nations that do not operate with a federal system, the process to petition the supreme court is fairly similar. Generally, the highest courts in these nations exist entirely to hear cases that concern its constitution. China, however, provides a unique example where it has three separate courts to hear different matters — one court for civil and criminal cases, one court for executive cases, and one constitutional court. Petitioning any of these three courts requires a similar process whereby you will have had to exhaust all other avenues of appeal prior to filing your case. Further, because each court only hears a particular class of case, you will have to discern the appropriate court in which to file.
One thing every litigant must keep in mind when deciding whether or not to petition the supreme court is the cost involved in conjunction with the unlikelihood of having the case heard. Unless the Court is willing to grant, as they are in limited circumstances, a waiver of costs — called filing in forma pauperis — for litigants who do not have the funds to pay the expensive filing fee and associated court costs, then filing a petition to the supreme court is an expensive process. These costs, mostly in the form of attorney’s fees, can be extensive even if the court declines to hear your case.