Determination of an assessed value is a complicated process. A tax assessor (a licensed professional) gives an opinion of value in accordance with the basis of real property value recognized by state law.
In New Jersey, each town uses different percentage of the market value as an assessed value. For example, West Windsor used 97% of the market value, whereas, Lawrence township uses only 52%.
A bank will have the property appraised and will (most likely) not issue a loan greater than the appraised value of the property, which may or may not be the same as assessed value or the sale price. Thanks.