The stimulus-responsive behavior of coordination networks (CNs), which switch between closed (nonporous) and open (porous) phases, is of interest because of its potential utility in gas storage and separation. Herein, we report two polymorphs of a new square-lattice (sql) topology CN, X-sql-1-Cu, of formula [Cu(Imibz)₂]_n (HImibz = {[4-(1H-imidazol-1-yl)phenylimino]methyl}benzoic acid), isolated from the as-synthesized CN X-sql-1-Cu-(MeOH)₂·2MeOH, which subsequently transformed to a narrow pore solvate, X-sql-1-Cu-A·MeOH, upon mild activation (drying in air or heating at 333 K under nitrogen). X-sql-1-Cu-A·MeOH contains MeOH in cavities, which was removed through exposure to vacuum for 2 h, yielding the nonporous (closed) phase X-sql-1-Cu-A. In contrast, a more dense polymorph, X-sql-1-Cu-B, was obtained by exposing X-sql-1-Cu-(MeOH)₂·2MeOH directly to vacuum for 2 h. Gas sorption studies conducted on X-sql-1-Cu-A and X-sql-1-Cu-B revealed different switching behaviors to two open phases (X-sql-1-Cu·CO₂ and X-sql-1-Cu·C₂H₂), with different gate-opening threshold pressures for CO₂ at 195 K and C₂H₂ at 278 K. Coincident CO₂ sorption and in situ powder X-ray diffraction studies at 195 K revealed that X-sql-1-Cu-A transformed to X-sql-1-Cu-B after the first sorption cycle and that the CO₂-induced switching transformation was thereafter reversible. The results presented herein provide insights into the relationship between two polymorphs of a CN and the effect of polymorphism upon gas sorption properties. To the best of our knowledge, whereas sql networks such as X-sql-1-Cu are widely studied in terms of their structural and sorption properties, this study represents only the second example of an in-depth study of the sorption properties of polymorphic sql networks.