Long-range order and phase transitions in two-dimensional (2D) systems-such as magnetism, superconductivity, and crystallinity-have been important research topics for decades. The issue of 2D crystalline order has reemerged recently, with the development of exfoliated atomic crystals. Understanding the dimensional limit of crystalline phases, with different types of bonding and synthetic techniques, is at the foundation of low-dimensional materials design. We study ultrathin membranes of SrTiO3, an archetypal perovskite oxide with isotropic (3D) bonding. Atomically controlled membranes are released after synthesis by dissolving an underlying epitaxial layer. Although all unreleased films are initially single-crystalline, the SrTiO3 membrane lattice collapses below a critical thickness (5 unit cells). This crossover from algebraic to exponential decay of the crystalline coherence length is analogous to the 2D topological Berezinskii-Kosterlitz-Thouless (BKT) transition. The transition is likely driven by chemical bond breaking at the 2D layer-3D bulk interface, defining an effective dimensional phase boundary for coherent crystalline lattices.