It is illegal to possess any wild animal who naturally lives in the state (ie., squirrels, crows, deer) unless you are transporting the animal to a licensed wildlife rehabilitator for care. It is illegal to provide rehabilitation to a sick, injured or orphaned wild animal without proper permits and licenses.
Senate bill sb-1504 and house bill hb-2901 were both proposed legislation allowing the private ownership of Texas state deer.
Here's an interesting article to read that is concerning the point I have been trying to make.
It even has pretty pictures to look at
http://www.wfaa.com/news/local/Who-owns-all-deer-in-Texas-You-may-be-surprised-111499214.html
