The person that is legally obligated to authorize the disposition or human remains is governed by Texas Health and Safety Code 711.02.  It states:

Sec. 711.002. DISPOSITION OF REMAINS; DUTY TO INTER. (a) Except as provided by Subsection (l), unless a decedent has left directions in writing for the disposition of the decedent’s remains as provided in Subsection (g), the following persons, in the priority listed, have the right to control the disposition, including cremation, of the decedent’s remains, shall inter the remains, and are liable for the reasonable cost of interment:

(1) the person designated in a written instrument signed by the decedent;

(2) the decedent’s surviving spouse;

(3) any one of the decedent’s surviving adult children;

(4) either one of the decedent’s surviving parents;

(5) any one of the decedent’s surviving adult siblings; or

(6) any adult person in the next degree of kinship in the order named by law to inherit the estate of the decedent.

(a-1) If the person with the right to control the disposition of the decedent’s remains fails to make final arrangements or appoint another person to make final arrangements for the disposition before the earlier of the 6th day after the date the person received notice of the decedent’s death or the 10th day after the date the decedent died, the person is presumed to be unable or unwilling to control the disposition, and:

(1) the person’s right to control the disposition is terminated; and

(2) the right to control the disposition is passed to the following persons in the following priority:

(A) any other person in the same priority class under Subsection (a) as the person whose right was terminated; or

(B) a person in a different priority class, in the priority listed in Subsection (a).