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Christian Voice director Stephen Green is attempting to bring a private prosecution for blasphemy against director general Mark Thompson and the show's producer Jon Thoday.
Green claimed that the show contained scenes which "vilify God and the Bible". He originally took the case to the City of Westminster magistrates in January but was refused.
His legal representative Michael Gledhill QC has argued that the City of Westminster district judge made an error in not allowing the action, claiming that the programme "crossed the blasphemy threshold".
Today judges said that the court would take its time to reconsider the case and would give a written verdict at a later date.
The BBC received 63,000 complaints after screening the musical on BBC Two in January 2005.
