Conn. Gen. Stat. § 54-131k: Compassionate parole release.

(a) The Board of Pardons and Paroles may grant a compassionate parole release to any inmate serving any sentence of imprisonment, except an inmate convicted of a capital felony under the provisions of section 53a-54b in effect prior to April 25, 2012, or murder with special circumstances under the provisions of section 53a-54b in effect on or after April 25, 2012, if it finds that such inmate (1) is so physically or mentally debilitated, incapacitated or infirm as a result of advanced age or as a result of a condition, disease or syndrome that is not terminal as to be physically incapable of presenting a danger to society, and (2) (A) has served not less than one-half of such inmate's definite or aggregate sentence, or (B) has served not less than one-half of such inmate's remaining definite or aggregate sentence after commutation of the original sentence by the Board of Pardons and Paroles.

(b) Any person granted a compassionate parole release pursuant to this section shall be released subject to such terms and conditions as may be established by the Board of Pardons and Paroles and shall be supervised by the Department of Correction.