Karen's answer is right on the mark. There are many factors that might come into play with the city's valuation of the property vs. what fair market value is in today's market. I always believe the fair market assessed value will be it's most accurate in the year following a recorded sale. Why? Because one of the forms both buyer and seller signs at closing is a document that alerts the taxing authorities as to the sale price. Market value is truly what a ready, willing and able buyer is willing to pay and what a motivated seller is willing to sell for, therefore, the most accurate way to determine "market value" would be a study of the most recent sales of comparable properties.
If a property hasn't sold in many years, it's quite typical that the fair market assessed value will be significantly lower than what current market value truly is. Although, in some Madison neighborhoods we're seeing assessed values much higher than true sale prices. An indication of a market adjustment. In many cases, these neighborhoods were "hot" during the boom of 2004-mid 2006. The tax assessor was keeping up with these sales and adjusting all properties similar to these prices. Now that the market adjustment is occuring, many of these homeowners are over-assessed and should contact the city for an adjustment back down.
Confused? It's not an easy answer but suffice to say the best indication of market value is what someone is willing to sell for and what someone is willing to pay.