An eviction must be filed in the Justice precinct where the rental property is located. Texas Property Code, Sec.Fill out the Landlord's Sworn. Motion for Writ of Possession and Notice of Hearing and sign it in front of a notary. If the judge ruled against you in the initial eviction suit in justice court, you have the opportunity to appeal. Please contact your tax agent for a copy of the notice. If they do not vacate in the notice period, you will then file for an eviction at your local small claims court. Learn the virtual court procedures, who you need to contact, and more about the Travis County Civil District Courts. Rules of Civil Procedure and local Rule 2.4. A Texas landlord or property manager cannot begin an eviction lawsuit without first legally notifying the tenant of the basis for the eviction.