Not Legal Advice: You could probably get in trouble for shooting a Red-cockaded Woodpecker (Picoides borealis) as this is under the Federal and State Listed Birds in Texas, categorized under threatened species.
Current listing maintained on file with the Secretary of State. Copies may be acquired by contacting TPWD's Wildlife Diversity Program at Austin headquarters. Restrictions apply to the possession of legally acquired specimens of species listed as threatened or endangered in Texas.
All wild birds that migrate through or are indigenous to Texas, along with their plumage or other parts, eggs, nests and young are protected from harming, killing and/or possession by state and federal law except that European starlings, English sparrows, and feral pigeons may be killed at any time and their nests and eggs may be destroyed.
A permit is not required to control grackles; cowbirds; yellow-headed, red-winged, rusty or Brewer's blackbirds; crows or magpies when these birds are considered a nuisance or causing a public health hazard. No birds may be controlled by any means considered illegal by local city or county ordinance.
For more info, visit tpwd.texas.gov.