Yep, when we bought our house in CA the taxes on the house doubled when we bought it. The previous owners lived in the house 17 years and had totally remodeled the house.
To expand: When we bought the house the assessment was based on OUR purchase price of the house, minus exemptions (about 10K.) So basically until we sold it in 2006, the assessed value (and taxes) increased about 2 percent every year. When we sold the house at nearly double the price for which we purchased it, the new owner got nailed for HIS purchase price--meaning the taxes went from about $4K/year under us to $8K/year, and when the housing market tanked, people are still paying taxes on homes that assessed for 30-40 percent above what they're worth.
Oh, sure--you can go to the county and apply for relief. Good luck getting it.
Granted, property taxes in NH suck, but at least the property is assessed every five years (max.) and tax rates adjusted to meet budgetary requirements. I never liked how CA did it--send all the money to the county, who sends it to Sacramento, who then tells the cities/counties how much they're going to get.