Now you have me thinking -- I think it isn't just voting precinct either, but cities as well. I'm not 100% sure of this but I recall signing a petition for Euless to sell wine because everyone was crossing the street into Grapevine to buy it (wave bye bye to the tax money).
I'll do some more reading -- I'm betting though that it may be city, precinct, county, state -- all of the above.
Well, it turns out that we're both right.
http://www.sos.state.tx.us/elections/laws/liquorelections.shtml