Conn. Gen. Stat. § 31-228: Benefit for total unemployment.

An eligible individual who is totally unemployed throughout a week, which shall be, at the discretion of the administrator, either a calendar week or a payroll week of seven consecutive days as determined by the administrator, shall be paid, with respect to such week, an amount equal to his total unemployment benefit rate for the benefit year during which such week of unemployment occurs. An individual shall be deemed to be totally unemployed throughout a week if he has performed during that week no services for which remuneration of any nature is payable, except service performed in the employ of any town, city or other political subdivision, which service is performed in lieu of payment of any delinquent tax payable to such town, city or other political subdivision and for which no other remuneration is payable and has not engaged in any self-employment.