Statute, §30-3A-3.1, Overview. Unlike harassment and stalking, aggravated stalking is a felony level offense only. The district courts, therefore, have exclusive jurisdiction to preside over these cases.Basically, aggravated stalking is stalking which is conducted in specific ways.As provided in §30-3A-3.1, aggravated stalking consists of stalking perpetrated as follows:he district courts, therefore, have exclusive jurisdiction to preside over these cases. Basically, aggravated stalking is stalking which is conducted in specific ways. As provided in §30-3A-3.1, aggravated stalking consists of stalking perpetrated as follows: