In TX, only those who voted in the election can vote in the runoff.
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Where in the world did you dig that erronous info up?
From the Texas SOS website:
http://www.sos.state.tx.us/about/newsreleases/2014/051614.shtml
If you voted in a party primary or participated in a convention, you can only vote in
that same partys runoff said Secretary Berry. If you did not vote in the March 4 Primary you
may still vote and can vote in the runoff election for either party. said Secretary Berry.
BTW, it makes sense.