In Texas, I believe that if you do not have a CHL and you have a weapon in the vehicle, the weapon has to be secured outside of one's arm reach.
For the record, this is an incorrect statement of Texas law.
"Sec. 46.02. UNLAWFUL CARRYING WEAPONS. (a) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun, illegal knife, or club if the person is not:
(1) on the person's own premises or premises under the person's control; or
(2) inside of or directly en route to a motor vehicle that is owned by the person or under the person's control.
(a-1) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun in a motor vehicle that is owned by the person or under the person's control at any time in which:
(1) the handgun is in plain view; or
(2) the person is:
(A) engaged in criminal activity, other than a Class C misdemeanor that is a violation of a law or ordinance regulating traffic;
(B) prohibited by law from possessing a firearm; or
(C) a member of a criminal street gang, as defined by Section 71.01."
The weapon cannot be in plain view, other than that, you are OK as long as you can legally possess the weapon and aren't doing something illegal.
And while currently, Texas does not require you to notify a LEO that you have a CHL, I believe that it is in one's best interest to do so.
This is also an incorrect statement of Texas law.
"Sec. 411.205. REQUIREMENT TO DISPLAY LICENSE. If a license holder is carrying a handgun on or about the license holder's person when a magistrate or a peace officer demands that the license holder display identification, the license holder shall display both the license holder's driver's license or identification certificate issued by the department and the license holder's handgun license. "