Texas Finance Code - FIN § 59.106. Access by More Than One Person

(a) If a safe deposit box is leased in the name of two or more persons jointly or if a person other than the lessee is designated in the lease agreement as having a right of access to the box, each of those persons is entitled to have access to the box and to remove its contents in the absence of a contract to the contrary.  This right of access and removal is not affected by the death or incapacity of another person who is a lessee or otherwise entitled to have access to the box.

(b) A safe deposit company is not responsible for damage arising from access to a safe deposit box or removal of any of its contents by a person with a right of access to the box.