Sec. 24.60055. 513TH JUDICIAL DISTRICT (HARRIS COUNTY). (a) The 513th Judicial District is composed of Harris County. (b) The 513th District Court shall give preference to civil cases. Added by Acts 2025, 89th Leg., 2nd C.S., Ch. 7 (H.B. 16), Sec. 1.17(a), eff. September 1, 2026.