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A new two-dimensional (2D) coordination polymer of the formula {Cu(ox)(4-Hmpz)·1/3H₂O}<i>_n</i> (<b>1</b>) (ox = oxalate and 4-Hmpz = 4-methyl-1<i>H</i>-pyrazole) has been prepared, and its structure has been determined by single-crystal X-ray diffraction. It consists of corrugated oxalato-bridged copper(II) neutral layers featuring two alternating bridging modes of the oxalate group within each layer, the symmetric bis-bidentate (μ-<i>κ</i>²<i>O</i>¹,<i>O</i>²:<i>κ</i>²<i>O</i>^2′,<i>O</i>^1′) and the asymmetric bis(bidentate/monodentate) (μ₄-<i>κO</i>¹:<i>κ</i>²<i>O</i>¹,<i>O</i>²:<i>κO</i>^2′:<i>κ</i>²<i>O</i>^2′,<i>O</i>^1′) coordination modes. The three crystallographically independent six-coordinate copper(II) ions that occur in <b>1</b> have tetragonally elongated surroundings with three oxygen atoms from two oxalate ligands, a methylpyrazole-nitrogen defining the equatorial plane, and two other oxalate-oxygen atoms occupying the axial positions. The monodentate 4-Hmpz ligands alternatively extrude above and below each oxalate-bridged copper(II) layer, and the water molecules of crystallization are located between the layers. Compound <b>1</b> exhibits a fast and selective adsorption of methylamine vapors to afford the adsorbate of formula {Cu(ox)(4-Hmpz)·3MeNH₂·1/3H₂O}<i>_n</i> (<b>2</b>), which is accompanied by a concomitant color change from cyan to deep blue. Compound <b>2</b> transforms into {Cu(ox)(4-Hmpz)·MeNH₂·1/3H₂O}<i>_n</i> (<b>3</b>) under vacuum for three hours. The cryomagnetic study of <b>1</b>–<b>3</b> revealed a unique switching from strong (<b>1</b>) to weak (<b>2</b> and <b>3</b>) antiferromagnetic interactions. The external control of the optical and magnetic properties along this series of compounds might make them suitable candidates for switching optical and magnetic devices for chemical sensing.