You'd have a screwed up system if it was OK to vote for a presidential contest twice.
7. Removal from Registration List: Under what circumstances can my name be removed from the list of registered voters?
Response: The county registrar shall cancel a voters registration immediately on receipt of any of the following:
...
notice from a voter registration official in another state that the voter has registered to vote outside the state of Texas
http://www.866ourvote.org/state/materials/TX-Manual-2012-FINAL.pdf
If it were legal, the Republicans wouldn't have dropped him. He voted in the general election, just just primaries, in both states:
http://www.juanitajean.com/2013/03/28/an-open-letter-to-cathy-engelbrecht-queen-of-true-the-vote/
As the Texas voting site points out, people who may have a claim to be resident in 2 states, such as students, have to choose:
Lesson One: You have to register
If youre a student who spends several weeks or months a year in different locations but wants to vote in Texas, youll need to decide which place in Texas is the place you call home, i.e., where you intend to return after youve been away. If you consider your parents address to be your permanent residence, you may use that address as your registration address. If you would like to register to vote at your college address, you may do so, but you cant be registered in both places.
If you consider yourself a permanent resident of another state, youll need to consult with officials there for registration and ballot-by-mail procedures.
http://votetexas.gov/voting/#students