Texas Tax Code - TAX § 26.112. Calculation of Taxes on Residence Homestead of Certain Persons

(a) Except as provided by Section 26.10(b), if at any time during a tax year property is owned by an individual who qualifies for an exemption under Section 11.13(c) or (d), 11.133, or 11.134, the amount of the tax due on the property for the tax year is calculated as if the individual qualified for the exemption on January 1 and continued to qualify for the exemption for the remainder of the tax year.

(b) If an individual qualifies for an exemption under Section 11.13(c) or (d), 11.133, or 11.134 with respect to the property after the amount of the tax due on the property is calculated and the effect of the qualification is to reduce the amount of the tax due on the property, the assessor for each taxing unit shall recalculate the amount of the tax due on the property and correct the tax roll.  If the tax bill has been mailed and the tax on the property has not been paid, the assessor shall mail a corrected tax bill to the person in whose name the property is listed on the tax roll or to the person's authorized agent.  If the tax on the property has been paid, the tax collector for the taxing unit shall refund to the person who was the owner of the property on the date the tax was paid the amount by which the payment exceeded the tax due.