Insulation, Radiant and Vapor Barriers - ? need for vapor barrier on interior bathroom wall

We are adding on a bathroom and have insulated all exterior walls with R-19 as well as a plastic vapor barrier. However, the bathroom has 2 interior walls that we would like to put some sound deadening insulation into. Do we need to put a vapor barrier on the inside(bathroom side) of these walls? They will have greenboard on them.
Also, the insulation we used was faced with paper, but we also added the poly vapor barrier on the interior surface as added protection. There's no problem with that, is there?
we live in CT
Thanks.
Dave

The purpose of the vapor retarder, which is placed facing the heated side of the structure, is to prevent warm, humid air from entering cold, exterior wall cavities where it will condense and cause insulation to lose insulative properties when it gets wet and wood decay in cavity. Interior walls would not have to have vapor retarder because they are within the heated space. Use concrete underlayment board in tub/shower area. Green board is water resistant, but not waterproof.

Thanks. And the plastic over the paper vapor barrier should be okay? we just figured it would stop air infiltration, etc better.
I know not to put a vapor barrier on top of insulation (sandwiching insulation between vapor barriers), but I believe this should be fine, right?

Sounds like double protection.