Yes, you can rent out your permanent residence tax home while temporarily working out of state. You will have to report the rental income on your tax return, but it won't have any effect on your Texas residency.
What makes you a resident? Generally, you're a resident of a state
if you intend to either stay there permanently, or return there after
a temporary absence. It's where home is – where you come
back to after being away on vacation, business trip, temporary employment out-of-state, overseas employment, or school. Many factors are considered, not
the least of which are where you are registered to vote, own homestead property
and are licensed to drive.
