Your taxes are based on your assessment. Assessments typically change when either the county does a county wide reassessment or you take out a building permit. Upon completion of the work, your taxes may go up based on the value of the work they permit allotted for.
Your best source for this will be the town:
For more information or to contact you municipality, please visit http://www.stlawrenceproperties.net/ and click on Area Information.