Federal and state constitutions already guarantee the supremacy of U.S. law in domestic cases but when he introduced the bill in 2011, Cleveland told The News & Observer that he was concerned about Shariah law gaining a foothold in communities with large Muslim populations.
The current bill does not mention Shariah law which governs the conduct of an observant Muslim's life and is the basis for the legal code in some countries in the Middle East and Asia.
In the past, critics of such bills have argued that they could make it difficult for multinational corporations who do business in the state.
The bill is in the House Judiciary Committee.
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