Is it true that non-Muslims are punished under sharia according to their holy book (e.g., the Bible)?

I've heard this story a few times, and I'm wondering if it's actually true. Basically, the story goes something like: a non-Muslim was being punished under sharia, but instead of using the Qur'an, the judge used the non-Muslim's holy book for sentencing. **Question**: Is it true that non-Muslims are punished under sharia according to their holy book (e.g., the Bible)?