Texas keeps it nice and simple. Pole, line, and hook.

From the Texas Parks & Wildlife Web site

Pole and Line:
A line with hook, attached to a pole (includes rod and reel)
•May be used to take GAME AND NONGAME fish.
•It is unlawful to take or attempt to take fish with one or more hooks attached to a line or artificial lure used in a manner to foul-hook a fish (snagging or jerking). A fish is foul-hooked when caught by a hook in an area other than the fish's mouth.
•Game and nongame fish may be taken by pole and line, except that in the Guadalupe River in Comal County from the second bridge crossing on River Road upstream to the easternmost bridge crossing on FM Road 306, rainbow and brown trout may not be retained when taken by any method except artificial lures. In this area only, artificial lures cannot contain or have attached either whole or portions, living or dead, of organisms such as fish, crayfish, insects (grubs, larvae or adults) or worms, any other animal or vegetable material, or synthetic scented materials. This does not prohibit the use of artificial lures that contain components of hair or feathers. It is an offense to possess rainbow and brown trout while fishing with any other device in that part of the Guadalupe River defined in this paragraph.
•Pole and line is the only lawful method for taking game and nongame fish from Community Fishing Lakes, sections of rivers lying totally within boundaries of a state park, the North Concho River from O.C. Fisher dam to the Bell Street dam, the South Concho River from Lone Wolf dam to Bell Street dam, and Lake Pflugerville.

I emailed the fellow that is in charge of state and water body records in Texas. I was told that Tenkara would fall in the category "other methods." It does not qualify for "catch & release." The catch would have to be measured, weighed on state certified scales, pictures taken, and have a witness to sign the application. My nearest scales would be over 30 miles away - nice dead fish!
The only reason it is not fly fishing - no reel. It is lumped with cane poles, trot lines, jug lines, spears, and others.

Bob