I recently looked at all the assessment prices and all the sales prices for a range of homes sold in one particular MA town, and I found the following:
1. About half of the time, assessment was higher than purchase price, about half the time lower.
2. Nearly half of the time, the difference was drastic (greater than 10 percent).
3. The most extreme differences were in cases where the purchase price was much lower than the assessment value.
Based on my very limited data set, it seems that assessment value is slightly less effective than, say, the Zillow estimates as a predictor of sale value (though it is a good predictor of what you will pay in taxes).
You can do a similar check for your town (using online tools like trulia, redfin, zillow, eppraisal, etc.)
And take it all with a grain of salt. For many purposes (say, determining which neighborhoods are pricier than others), crude ballpark figures are enough --- but when you're deciding how much to offer for a home, you probably shouldn't be happy with an estimate that leads you to overpay by 20% a good fraction of the time.
If your question is about negotiation psychology (e.g., you want to give a lowball offer legitimacy by pointing out to the seller that you are, after all, offering the assessment price), then you should also add that you believe that a more careful CMA supports the assessment value (if this is indeed the case). But in the end, your ability to get the home at a lower price will depend on the seller's motivations and on how much interest other people are showing in the house at the current listing price. (Are there already three offers near or above the listing price? Or are there no offers --- with the house sitting around for months, sometimes going entire weeks without a single showing?) This is information that the seller has and you don't (though the listing agent may be willing to give you hints, if it is in the seller's best interest to do so) --- and it has little to do with assessment value.