Ok, so know you are in area that I know something about.
Valuations and the time frame for what they cover are different not just in every state, but in every county. What affects your property taxes mostly is the mill rate (rate per 100 or 1000 assessed). In the current housing downturn, housing values trail in your tax assessments by at least a year.
The problem is that counties need money to operate, so what you will commonly see is a reduction in the assessment but an increase in the millrate (expect taxes to grow at 2.5% annually).
If you disagree with the assessment on your house, you can appeal to your local tax board (or whatever it is called in your county). They can reset (generally both higher or lower) the assessed value of your home.
You absolutely will not see a big reduction in property taxes just because your house value plummeted. If counties did that services would come to a screaching halt. You can complain about taxes all day long, but it is the responsibility of ever member of a democracy to support it. Paying taxes is the fee for a properly operating government.