You should be able to, as court cases are public record.
Lower courts, meaning trial courts (courts of original jurisdiction) or lower appellate courts.
kind of court? Criminal court for adults, Family court for kids. Civil court of found not guilty for shoplifting and your suing them.
Brown vs Board of Education
Depending on the type of court case you can take your case to the appelate court sytem in your state or a federal court of appeals