First of all, the value as listed on property taxes is NOT always the fair market value. That value is used when calculating your property tax payment. As a matter of fact that value was reflected the fair market value of your home maybe 5 or 6 years ago.
The local county will review and re-evaluate the home tax value maybe every now and then (might as long as 5 to 6 years) just to make sure the property tax they charged is on the fair market side. This value might reflect some degree of the home value if the local real estate market in your area is relatively stable in the past few years. But if you need a detailed analysis report about the current fair market value of your home you need always contact your realtor to run a CMA (comparative market analysis) report.