Conn. Gen. Stat. § 47a § 47a-39

Upon the hearing on such application in the Superior Court the judgment of the trial court shall stand, but upon such hearing if it appears that the premises, judgment for possession or occupancy of which has been rendered, are used for dwelling purposes and are not excluded by the provisions of section 47a-36; that the applicant cannot secure suitable premises for himself and his family elsewhere within the city or town or in a city or town adjacent thereto in a neighborhood reasonably comparable to that in which the premises occupied by him are situated; that he has used due diligence and reasonable effort to secure other premises; that his application is made in good faith, and that he will abide by and comply with such terms and provisions as the court may prescribe, the court may grant a stay of execution for a period or for periods in the aggregate not exceeding six months from the date of the judgment in the summary process action upon such conditions and terms as appear fair and equitable, except that such stay of execution shall not exceed three months in the aggregate if the reason for the judgment against the defendant was nonpayment of rent; provided in the case of an applicant who is a resident in a mobile manufactured home park and owns his own unit and has received notice pursuant to subparagraph (E) of subdivision (1) of subsection (b) of section 21-80 or an applicant who is a conversion tenant, as defined in section 47-283, or who at the time of conversion was residing in a dwelling unit in a building or on property which has been declared a conversion condominium, at the end of such six-month period the court may extend such stay of execution under the same or different conditions and terms for an additional period not exceeding nine months taking into consideration the age of the applicant, the size of the applicant's family, the length of time of such applicant's tenancy and the availability of suitable alternative housing. Such extended stay may be reviewed every two months. The court shall consider all the circumstances of the case, the equities involved and whether any undue hardship would result to either party. Such conditions and terms may include the requirement that the applicant shall pay to the plaintiff in the summary process action such amount in such installments from time to time and in such manner as the court may direct, for the use and occupancy of the premises for such period of the stay, at the rate to which he was liable as rent for the month immediately prior to the expiration of his term or tenancy, if any, and any assessment for current common expenses not already included in the rent as provided in subsection (b) of section 47-76, if any, or such sum as may be determined by the court to be reasonable for such use and occupancy. Such payment shall also include all rent unpaid prior to the period of such stay.