  There has been much recent interest into those properties of a 3-manifold
determined by the profinite completion of its fundamental group. In this paper
we give readily computable criteria specifying precisely when two orientable
graph manifold groups have isomorphic profinite completions. Our results also
distinguish graph manifolds among the class of all 3-manifolds and give
information about the structure of totally hyperbolic manifolds, and give
control over the pro-$p$ completion of certain graph manifold groups.
