Conn. Gen. Stat. § 25-89: New and supplementary assessments.

If any assessment is not valid or enforceable for any reason, a new assessment may be made in the manner hereinbefore provided for the determination of the original assessment. If any assessment is made which is not sufficient to cover the entire cost of the work to be paid for by such assessment, a supplementary assessment may be made by the board against those properties previously assessed, to the end that a sum sufficient to pay the cost of such work may be obtained, provided the total of such supplementary assessment and the original assessment shall not exceed the value of the special benefit to accrue to the property against which the benefit is assessed.