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Explanation: Some clarification further to my original proposed answer that may or may not help. The nature of criminal acts can be classified (in very basic terms) as follows:
crimes against persons (ex. assault, murder)
crimes against property (ex. arson, vandalism)
corporate crimes (ex. embezzlement)
In this case, "The Legislative Assembly of the Krasnoyarsk region has not given its consent for the criminal case against A.P.Bykov, who is accused of having committed a crime [or "criminal offence"] against a person, to be brought before the court." This is a bit "official", and if you want to reduce that connotation in the translation, you could simply state that he is accused of a "criminal offence".