Question

which supreme court case determined that the death penalty could not be used on people with mental disabilities?

Answer 1

Atkins v. Virginia

Atkins was convicted of abduction, armed robbery, and capital murder, but was verified as mentally disabled by a forensic psychologist. The jury sentenced him to death two times, after the first time was found to have a misleading verdict. However, despite the ruling of the jury, found that sentencing him to death would be "cruel and unusual punishment".

HOWEVER, Penry v. Lynaugh was another case earlier that ALSO determined the death penalty could not be used on people with mental disabilities. So it depends on the options you have.

I hope I've helped! :)