Taxes will not be adjusted unless you file a tax appeal with the municipality. In Connecticut the appeals process begins by requesting an appeals form and completing it and submitting it prior to the deadline of February 20th. Any owner of a property and Lessee with a lease that requires the payment of taxes may file an appeal. Photographs of defects and clear reasons why the property assessment is unfair, such as errors in square footage, number of baths and other fixtures and assets will be effective in persuading the board to reconsider the assessment.
It is possible to get the taxes adjusted. One of the things you can do is bring your purchase and sales agreement down to the local assesors office and talk with them directly. This will give you a much better idea of where you stand as the assessor will then tell you whether or not if reducing the taxes is even something the town would consider.
That's completely dependent on the local assessor. We bought a condo for 20% below assessed value, and the assessor wouldn't adjust a penny. A duplex we bought was adjusted down to exactly the purchase price. I wouldn't count on the taxes going down. If it's affordable and makes sense to you with the taxes, then consider it an added bonus if you get an adjustment. However, if you can't afford (or aren't willing) to pay the current taxes, don't buy the house.