A pre-requisite for NMR studies of organic materials is assigning each experimental chemical shift to a set of geometrically equivalent nuclei. Obtaining the assignment experimentally can be challenging and typically requires time-consuming multi-dimensional correlation experiments. An alternative solution for determining the assignment involves statistical analysis of experimental chemical shift databases, but no such database exists for molecular solids. Here, by combining the Cambridge structural database with a machine learning model of chemical shifts, we construct a statistical basis for probabilistic chemical shift assignment of organic crystals by calculating shifts for over 200,000 compounds, enabling the probabilistic assignment of organic crystals directly from their two-dimensional chemical structure. The approach is demonstrated with the 13C and 1H assignment of eleven molecular solids with experimental shifts, and benchmarked on 100 crystals using predicted shifts. The correct assignment was found among the two most probable assignments in over 80% of cases.