Texas Election Code - ELEC § 201.001. Resigning or Declining Office

(a) To be effective, a public officer's resignation or an officer-elect's declination must be in writing and signed by the officer or officer-elect and delivered to the appropriate authority for acting on the resignation or declination.  The authority may not refuse to accept a resignation.

(b) If the authority to act on a resignation or declination is a body, the resignation or declination may be delivered to the presiding officer of the body or to its clerk or secretary.

(c) An officer-elect who intends to qualify for the office but desires to resign at a subsequent date may submit a resignation in the same manner as an officer who has assumed office, and the vacancy may be filled in the same manner as if the resignation had been submitted after the officer-elect assumed office.