It is well-established that synapse formation involves highly selective chemospecific mechanisms, but how neuron arbors are positioned before synapse formation remains unclear. Using 3D reconstructions of 298 neocortical cells of different types (including nest basket, small basket, large basket, bitufted, pyramidal, and Martinotti cells), we constructed a structural model of a cortical microcircuit, in which cells of different types were independently and randomly placed. We compared the positions of physical appositions resulting from the incidental overlap of axonal and dendritic arbors in the model (statistical structural connectivity) with the positions of putative functional synapses (functional synaptic connectivity) in 90 synaptic connections reconstructed from cortical slice preparations. Overall, we found that statistical connectivity predicted an average of 74 ± 2.7% (mean ± SEM) synapse location distributions for nine types of cortical connections. This finding suggests that chemospecific attractive and repulsive mechanisms generally do not result in pairwise-specific connectivity. In some cases, however, the predicted distributions do not match precisely, indicating that chemospecific steering and aligning of the arbors may occur for some types of connections. This finding suggests that random alignment of axonal and dendritic arbors provides a sufficient foundation for specific functional connectivity to emerge in local neural microcircuits.