Must probate be performed in the state where the person died?

What is the name of your state (only U.S. law)?

I have been appointed the executor of the estate by will and live in Texas. The deceased passed away in North Carolina. Must I probate in North Carolina or can I probate in Texas?

North Carolina.

Well it's the state he resided in at the time of his death, not where he happened to have died. I suspect the answer is the same in your case however.