Even though Texas is a non-disclosure state, now most of the Appraisal Districts have access to the MLS. Even if you have a non-disclosed sale, they can see the list price and may base the tax on that price or some price around it. Chances are the tax value will go up. Appraised values typically come out in April/May and I believe final values delivered to the taxing authorities by July 1. You may get to slip by for a year or so depending on when they do their appraisal and when you close. This often happens with new homes. If you get in under the wire, be sure to set aside money for the increase in taxes the next year. This has caught many homeowners off guard. What can happen is the mortgage company under withholds escrow for taxes, then gets surprised by the tax bill the second year and tries to make up for the shortfall.