You most definitely can appeal the county's appraisal of your property. How to do so, and your odds of success will vary widely by your location, but I have successfully appealed the valuation on one of my rental properties.
I asked my realtor to provide me with recent sales of comparable homes in the neighborhood & provided them along with my appeal as evidence of what I felt a reasonable valuation should be. One of three things will happen: 1) Your appeal will be accepted, 2) It will be denied, or 3) you will be asked to come in & plea your case in front of the county assessor. In my case, the county accepted my appeal without needing to testify.
Look around your county assessor's website ... you will probably be able to find the form necessary for filing an appeal. If not, give them a call & they'll tell you the procedure.
The county generally uses a simplistic statistical model to do their valuations. Little to no human time is spent reviewing your home's value, so it's quite possible for their valuation to be unreasonable.
An appeal can take a bit of time & paperwork, but can definitely be worth the effort if the county's valuation is way off.
Hope this helps!
@mhoran_psprep Your point is well taken that in practice the relationship between sales prices & tax assessments is a bit more tenuous. The waters get muddy when property values have a large swing (like the past 5 years). When tax assessor's started seeing large drops in property values during the recession (and consequent drops in their budgets), I'm sure there was considerable pressure to prevent wholesale decreases in tax valuations. It's politically easier to "prop-up" falling valuations than to raise tax rates. However, the fact remains that the models that assessors use in determining property values are based on sales history - thus, I believe (and have found) that recent sales can be a persuasive piece of evidence in a property tax assessment appeal.