In Kentucky, the closest term would be Guilty but Mentally Ill.
http://www.lrc.ky.gov/statutes/statute.aspx?id=19692
From a criminal defense prospective, it isn't used too much in Western KY at trial. There is a very fine line to walk of trying to explain a defendant's mental problems while not necessarily making excuses for their actions.
It doesn't affect a defendant's sentence but does leave open the possibility of required treatment to some degree.
http://www.lrc.ky.gov/statutes/statute.aspx?id=19694