APPROVAL BY MAYOR AND RELATED CONDITIONS FOR ORDINANCE TO TAKE EFFECT.
Tex. LOC. GOV'T Code § 52.003.
in effect(a) Before an ordinance or resolution adopted by the governing body of the municipality may take effect, the ordinance or resolution must be placed in the office of the secretary of the municipality. The mayor shall sign the ordinances and resolutions that the mayor approves.
(b) If the mayor does not sign an ordinance or resolution before the fourth day after the date it is placed in the secretary's office and does not return the ordinance or resolution under Subsection (c), the ordinance or resolution takes effect as provided by law.
(c) If the mayor returns an ordinance or resolution to the governing body with a statement of objections before the fourth day after the date the ordinance or resolution is placed in the secretary's office, the governing body shall, on the return, reconsider the vote by which the ordinance or resolution was adopted. If a majority of the total number of members of the governing body, excluding the mayor, approve the ordinance or resolution on reconsideration and enter the votes in the journal of the governing body's proceedings, the ordinance or resolution may take effect.