When the market is flat there should be little change in the overall assessments. It is also possible for some areas of a municipality to increase in value, while others may decrease. It is important to remember that the assessor does not create the value. The real estate marketplace establishes the values. It is the assessor's duty and responsibility to understand these values and assess your property accordingly.
Assessors have nothing to do with deciding the total amount of taxes to be collected.
The assessor does not assess a tax. The assessor's legal responsibility is to determine the fair market value of your property, so that the tax burden can be fairly and equitably distributed. The tax rate is determined by all the various taxing entities - town, county, school, and special districts. The amount of tax attributable to each property is in proportion to that individual property's value. The property tax has always been considered relatively stable source of money because it does not fluctuate as do sales and income taxes.