Conn. Gen. Stat. § 8 § 8-45a

A housing authority, as defined in subsection (b) of section 8-39, in determining eligibility for the rental of public housing units may establish criteria and consider relevant information concerning (1) an applicant's or any proposed occupant's history of criminal activity involving: (A) Crimes of physical violence to persons or property, (B) crimes involving the illegal manufacture, sale, distribution or use of, or possession with intent to manufacture, sell, use or distribute, a controlled substance, as defined in section 21a-240, or (C) other criminal acts which would adversely affect the health, safety or welfare of other tenants, (2) an applicant's or any proposed occupant's abuse, or pattern of abuse, of alcohol when the housing authority has reasonable cause to believe that such applicant's or proposed occupant's abuse, or pattern of abuse, of alcohol may interfere with the health, safety or right to peaceful enjoyment of the premises by other residents, and (3) an applicant or any proposed occupant who is subject to a lifetime registration requirement under section 54-252 on account of being convicted or found not guilty by reason of mental disease or defect of a sexually violent offense. In evaluating any such information, the housing authority shall give consideration to the time, nature and extent of the applicant's or proposed occupant's conduct and to factors which might indicate a reasonable probability of favorable future conduct such as evidence of rehabilitation and evidence of the willingness of the applicant, the applicant's family or the proposed occupant to participate in social service or other appropriate counseling programs and the availability of such programs.