Tex. Loc. Gov't Code § 372.012

The area of a public improvement district to be assessed according to the findings of the governing body of the municipality or county may be less than the area described in the proposed boundaries stated by the notice under Section 372.009. The area to be assessed may not include property not described by the notice as being within the proposed boundaries of the district unless a hearing is held to include the property and notice for the hearing is given in the same manner as notice under Section 372.009.