To download a .pdf application for exemption for mailing, type "reasons of conscience" in the search bar at the following page: Texas Dep't of State Health Services : Immunizations
Once TDSHS has the application, it will take about a week to receive the form (or forms - you can request up to 5 forms per child). The form must be duly completed and notarized. The original, notarized form must be delivered to the school or other facility requiring it, where it will be kept on file - be sure to keep a copy. Should the exempt child change schools, the original, notarized form must be delivered to the new facility.
To view the Texas vaccine laws, go here.