Found king pigeon New Braunfels, TX.

[Kleiber]

Well, on a daily basis I take my pigeon Piper for little walks through the park, I noticed last week there was a pure white pigeon, very big. And it just sits on the ground, and it isn't scared of people at all (wondering if it's tame?) I was looking up what it may be, and i'm for sure it's a King pigeon. It's still at the park, i'm wondering if I need go back and see if it has a band on it. But it's very tame, you can even go up to it, it doesn't run. And no, it isn't hurt, and it can fly.
What do I need to do?
I know they aren't native to the New Braunfels area, so it has to be someone's, right?