In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The emph{global} dynamics naturally builds on this network of couplings and it is often excited by a noise input with nontrivial structure. The underlying network is unknown in many applications and should be inferred from observed data. We assume: i) emph{Partial observability}--- time series data is only available over a subset of the nodes; ii) emph{Input noise}--- it is correlated across distinct nodes while temporally independent, i.e., it is emph{spatially colored}. We present a emph{feasibility condition} on the noise correlation structure wherein there exists a consistent network inference estimator to recover the underlying fundamental dependencies among the observed nodes. Further, we describe a structure identification algorithm that exhibits competitive performance across distinct regimes of network connectivity, observability, and noise correlation.