Cropp tested positive for methamphetamine in a urine sample taken in a random test at a race meeting in Hamilton on May 7, 2005. She has been fighting a legal battle ever since.
A hearing by racing's Judicial Control Authority (JCA) was interrupted in February last year when her lawyers sought a judicial review through the court system to argue that the drug test was unlawful.
Justice Pamela Andrews dismissed Cropp's case against the judicial committee in the High Court and her decision was upheld by the Court of Appeal on September 27.
Cropp was granted leave to appeal to the Supreme Court and that hearing took place in March.
Her lawyer Alan Ivory argued that random drug tests breached a fundamental right to bodily privacy and integrity.
The court reserved its decision and the case is listed today.
