Board Thread:Theories and Speculation/@comment-3001903-20160803001752/@comment-25449165-20160914003844

The Reanimation Jutsu basically brings the dead soul back and implants them into a sacrificed body, with all previous techniques they had before their death. Rinne Tensei requires a Rinnegan, which when a user that had had it before their death and was brought back with Edo Tensei, will have it.

Normally using the technique will cause you do die. In Nagato's case, his soul went to the afterlife (thus why he was able to come back with Edo Tensei). I think that even if you're a Reanimation, you can still die after using Rinne Rebirth. Because if you think about it, Reanimations can sustain a lot of physical damage and regenerate (unless you get hit by a Truth Seeking Ball). But nothing says about sacrificing your soul. So yeah. If you try using Rinne Rebirth even while as a Reanimation, you will die and your soul goes back to the afterlife.