状 originally meant a 诉状 - a written legal complaint submitted to a magistrate. In imperial China, 状告 meant filing such a document with the yamen 衙门. The word survived into modern Chinese as a slightly more emphatic synonym of 起诉.
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状告 carries a flavor of righteous grievance - 'I'm taking you to court.' Compare neutral 起诉 (file a lawsuit) and 控告 (to accuse, often criminally). Common in news headlines about David-vs-Goliath disputes.
