Generally in the United States property values are public record. Go to the county/city/town website and determine how you can view the other values. Many (most) have their records online so they can be viewed using a map interface, or an address look up. Others may still require a trip to the courthouse or other government building. Look at houses that are the same model as yours, look at the ones that may have been built a year earlier, because they would be on their second appraisal cycle.
Your appeal will most likely be successful if you can show that your house has been appraised higher then identical models in the same subdivision. The fact that the tax appraisal is higher or lower than the purchase price is not-relevant. The county uses the tax appraisal and the tax rate to set their budget. They may have a history of setting all new properties at purchase price + x% and then as they move forward keeping them at sales value + x%. Other jurisdictions set the tax appraisal below the sales price.
There are deadlines, so check the government website or the tax bill for how to file an appeal.
- You have to spend time and money on the process and might not get any reduction in taxes. In my county the appeal is free. But they are required to physically visit and measure the property, which requires the homeowner to be present. If you disagree with the new appraisal, then it goes to a hearing board which meets in the evening.
- Your taxes might go up. If the database from the builder didn't mention the deck, or the pool, or the 3 car instead of the 2 car garage; the county can up the appraisal.