TexasCHLforum.com

I can't carry out into the street without my CHL, so you certainly wouldn't be able to leave your apartment without it. That is not your property. It is owned by the complex owners. Without your CHL in your pocket, you would not be able to show it to an officer and you would be charged for it.

§ 46.15. NONAPPLICABILITY. (a) Sections 46.02 and 46.03
do not apply to:
...
(b) Section 46.02 does not apply to a person who:
...
(2) is on the person's own premises or premises under
the person's control ...

For reference:

§ 46.02. UNLAWFUL CARRYING WEAPONS. (a) A person commits
an offense if he intentionally, knowingly, or recklessly carries on
or about his person a handgun, illegal knife, or club.
(b) Except as provided by Subsection (c), an offense under
this section is a Class A misdemeanor.
(c) An offense under this section is a felony of the third
degree if the offense is committed on any premises licensed or
issued a permit by this state for the sale of alcoholic beverages.

Apartments are finicky. While I can walk out into my front yard and have a firearm openly visible to any passersby, an apartment owner is confined only to their four walls. So I wouldn't recommend even stepping out of your door without a coverup.