Power distribution system operators require knowledge of power injections for accomplishing various grid dispatch tasks. Monitoring, collecting, and processing smart meter data across all grid nodes, however, may not be affordable given the communication and storage resources. In this context,
the problem of inferring injections at all nodes by polling smart meter data from a subset of them is considered here. For non-synchronized grid data, including (re)active injections and nodal voltage magnitudes, intuitive topological and numerical observability criteria are provided. For the case
of synchrophasor data where nodal voltage angles are additionally known, the improvements in identifiability are also characterized. The analysis relies on the linearized power flow model and extends the traditional concept of observability in power transmission systems to radial distribution grids. The derived criteria are numerically validated on the IEEE 123-bus benchmark feeder.