Let's see if this can help you out:
Texas procedure generally
In Texas, the district courts have original jurisdiction for all criminal felony cases. If an individual is convicted of a capital felony, he or she may be subject to punishment by death, if the State sought such punishment. A capital felony is one in which an individual "intentionally or knowingly causes the death of an individual," under special circumstances. In particular, the: murder of a public safety officer, firefighter, or correctional employee; murder during the commission of specified felonies (kidnapping, burglary, robbery, aggravated rape, arson); murder for remuneration; multiple murders; murder during prison escape; murder of a correctional officer; murder by a state prison inmate who is serving a life sentence for any of five offenses; [or] murder of an individual under six years of age.
In Texas, a person must be of at least 17 years of age at the time of the crime to have the death penalty imposed upon him or her.
After the verdict is rendered, if the defendant is found guilty, the case is automatically appealed to the Court of Criminal Appeals.
Did you see the bold and underlined portion? That's where you seem to have the glitch.