Tex. Tax Code § 31.05

(a) The governing body of a taxing unit may adopt the discounts provided by Subsection (b) or Subsection (c), or both, in the manner required by law for official action by the body. The discounts, if adopted, apply only to that taxing unit's taxes. If a taxing unit adopts both discounts under Subsections (b) and (c), the discounts adopted under Subsection (b) apply unless the tax bills for the unit are mailed after September 30, in which case only the discounts under Subsection (c) apply. A taxing unit that collects taxes for another taxing unit that adopts the discounts may prepare and mail separate tax bills on behalf of the adopting taxing unit and may charge an additional fee for preparing and mailing the separate tax bills and for collecting the taxes imposed by the adopting taxing unit. If under an intergovernmental contract a county assessor-collector collects taxes for a taxing unit that adopts the discounts, the county assessor-collector may terminate the contract if the county has adopted a discount policy that is different from the discount policy adopted by the adopting taxing unit.

(b) A taxing unit may adopt the following discounts to apply regardless of the date on which it mails its tax bills:

(1) three percent if the tax is paid in October or earlier;

(2) two percent if the tax is paid in November; and

(3) one percent if the tax is paid in December.

(c) A taxing unit may adopt the following discounts to apply when it mails its tax bills after September 30:

(1) three percent if the tax is paid before or during the next full calendar month following the date on which the tax bills were mailed;

(2) two percent if the tax is paid during the second full calendar month following the date on which the tax bills were mailed; and

(3) one percent if the tax is paid during the third full calendar month following the date on which the tax bills were mailed.

(d) The governing body of a taxing unit may rescind a discount adopted by the governing body in the manner required by law for official action by the body. The rescission of a discount takes effect in the tax year following the year in which the discount is rescinded.