The 2009 Assessments and real estate tax bills came out recently. If you feel that the assessment of your property is overestimated or inaccurate you should file an abatement with the assessors office. Forms can be found here and must be returned to the assessors office (I believe by Feb 2 2009, although deadlines may vary).
View Fall River Property Information (including assessments) HERE
Also for information on the tax rate increase see: