I am native to the USA, which is where I still live but I'm not native to the state that I live in.
Nothing wrong with Tyto Alba's answer, but---
I've heard of "native land," but not "native place." (See the poem: http://www.bartleby.com/101/547.html)
So when I searched for it, I may have found out why:
"its use ("native place") seems limited to Indian English"
http://www.usingenglish.com/forum/threads/156069-Correct-meaning-of-Native-Place