First of all, Texas does not have any state taxes. You do not need to file one.
Generally speaking, if your permanent address is outside the US and you earned no US-sourced income, you would not file a State Income tax return. However, there are exceptions. For example, if you are a California resident and live overseas, California still considers you a resident for tax purposes until you've been absent from the state at least 546 consecutive days.
Hope it helps! Otherwise, please write back with more information for further assistance.