Nancy Grace says the double homicides of Rob Reiner and Michele Singer Reiner are a textbook example of a case that calls for the death penalty … and that could be bad news for alleged murderer Nick Reiner.

Nancy tells TMZ … this case is the classic example of when capital punishment should be applied, but that doesn’t mean it’s going to happen.

Los Angeles District Attorney Nathan Hochman mentioned the death penalty in a recent press conference, so it’s being talked about among prosecutors … but as Nancy explains, a final decision on capital punishment goes way beyond the D.A. office.

Nick is charged with murdering his parents at their Brentwood home … and he’s being held without bail and is on suicide watch as he awaits his January arraignment. He’s hired famed defense attorney Alan Jackson.