Is a person who is not of sound mind obligated to perform ghusl?

For a person to be religiously accountable, it is required that they possess sound mental faculties and have reached the age of puberty. Anyone who possesses these two qualities is considered religiously responsible.

Those who are not of sound mind do not possess this quality, and therefore are not obligated to perform religious duties such as ghusl, wudu, or prayer. (Ebû Dâvûd, Hudûd, 16 [4403]; Tirmizî, Hudûd, 1 [1423]; Abdülazîz el-Buhârî, Keşfü’l-esrâr, 4/371-373)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu