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Molecular dynamics simulations for a thin film of water confined to a slit nanopore are performed in order to investigate the dynamic process of crystallization of the system. The system upon freezing creates a bilayer ice crystal composed of two layers of hexagonal rings. We perform one simulation at T=257 K during which the system remains a supercooled liquid state, and another one at T=253 K during which the system freezes. Many patterns of molecular arrangement are found upon freezing, and an account is given of the origin of multiple peaks in the distributions of binding energy and pair interaction energy. A definition of the solidlike cluster is introduced in order to analyze the time evolution of the clusters’ population and their shapes. A large variety of shapes including highly nonspherical ones can be detected during simulations. A steady population of clusters is found at T=257 K, whereas at T=253 K a post-critical nucleus of the solid phase emerges within a few nanoseconds and continues to grow until the system freezes completely.