The statutes requires a person "(7) is not incapable of exercising sound judgment with respect to the proper use and storage of a handgun;"
This is defined a little later as:
6 GC §411.173. TEXAS CONCEALED HANDGUN LAWS (d) For purposes of Subsection (a)(7), a person is incapable of exercising sound judgment with respect to the proper use and storage of a handgun if the person:
(1) has been diagnosed by a licensed physician as suffering from a psychiatric disorder or condition that causes or is likely to cause substantial impairment in judgment, mood, perception, impulse control, or intellectual ability;
(2) suffers from a psychiatric disorder or condition described by Subdivision (1) that:
(A) is in remission but is reasonably likely to redevelop at a future time; or
(B) requires continuous medical treatment to avoid redevelopment;
(3) has been diagnosed by a licensed physician, determined by a review board or similar authority, or declared by a court to be incompetent to manage the person's own affairs; or
(4) has entered in a criminal proceeding a plea of not guilty by reason of insanity.
(e) The following constitutes evidence that a person has a psychiatric disorder or condition described by Subsection (d)(1):
(1) involuntary psychiatric hospitalization;
(2) psychiatric hospitalization;
(3) inpatient or residential substance abuse treatment in the preceding five-year period;
(4) diagnosis in the preceding five-year period by a licensed physician that the person is dependent on alcohol, a controlled substance, or a similar substance; or
(5) diagnosis at any time by a licensed physician that the person suffers or has suffered from a psychiatric disorder or condition consisting of or relating to:
(A) schizophrenia or delusional disorder;
(B) bipolar disorder;
(C) chronic dementia, whether caused by illness, brain defect,
or brain injury;
(D) dissociative identity disorder;
(E) intermittent explosive disorder; or
(F) antisocial personality disorder.
(f) Notwithstanding Subsection (d), a person who has previously been diagnosed as suffering from a psychiatric disorder or condition described by Subsection (d) or listed in Subsection (e) is not because of that disorder or condition incapable of exercising sound judgment with respect to the proper use and storage of a handgun if the person provides the department with a certificate from a licensed physician whose primary practice is in the field of psychiatry stating that the psychiatric disorder or condition is in remission and is not reasonably likely to develop at a future time.