Prosecutors say the veil will deny the defendant the right to a fair trial.
The case began in 2007 when the Toronto victim, referred to only as N.S., alleged that she was raped by her uncle and cousin when she was a child, The (Toronto) Globe and Mail reported.
During a preliminary inquiry, an Ontario judge denied the woman's request to wear her veil, which covers her face, while testifying. That ruling was overturned by the Ontario Court of Appeal, and has now been passed on to the Supreme Court.
Douglas Usher, a lawyer for one of the two accused men, said seeing a witness' facial reactions during testimony is critical and can go against a witness' credibility in the eyes of a judge or jury.
Experts watching the case have warned against an outcome that could have regrettable effects on future cases involving religious rights.
Frank Addario, a lawyer for the Criminal Lawyers Association, said: "The next claimant who asserts that his religion forbids him being tried by a female judge or a Christian judge will have to have his claim heard."
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