Conn. Gen. Stat. § 9-207: Library directors.

Any municipality, after establishing a library under the provisions of sections 11-20 and 11-21, shall at the first regular municipal election after the establishment of such library, elect one-third of the directors to hold office until the next such election, one-third until the second such election and one-third until the third such election, and, at all such elections of such municipality thereafter, one-third of the directors shall be elected to hold office for six years.