Keep in mind the Tax Office has never seen the inside of the house. Tax appraisals, sadly are not a good indication of the actual value of a home. Over a long period in real estate, I have seen Tax values all over the map. A homeowner only ever becomes concerned when the taxable value exceeds the market value.
I can expect to hear from about 10 or so past clients every year when the new appraisal values go out from the tax office, and those are usually cases where the tax appraisal value exceeds the market value.
In no way do I pay attention to tax values, even as a general guideline for pricing a property. Occasionally, I will see a tax value on a home that is pretty much representative of the market value, but it is rare.
Texas is a closed record state, so the tax office does not have access to actual sales prices being verified by title companies.
I often find clients believing in information from Zillow. Estimates of what a home is worth. The Zillow Zestimate (estimate) is based on a California Model. California is an open record state and the tax authorities have direct access to actual sales prices, so the tax values are pretty accurate.
A cash buyer in Texas can fool a tax authority real easy since there is not even a paper trail of a loan filed at the courthouse and no appraisal being done. I know of one such expensive home that is being taxed a 65% of it's market value.