Two-dimensional (2D) lead halide perovskites are a family of materials at the heart of solar cell, light-emitting diode, and photodetector technologies. This perspective leads to a number of synthetic efforts toward materials of this class, including those with prescribed polar architectures. The methylhydrazinium (MHy+) cation was recently presumed to have an unusual capacity to generate non-centrosymmetric perovskite phases, despite its intrinsically nonchiral structure. Here, we witness this effect once again in the case of the Ruddlesden-Popper perovskite phase of formula MHy2PbCl4. MHy2PbCl4 features three temperature-dependent crystal phases, with two first-order phase transitions at T1 = 338.2 K (331.8 K) and T2 = 224.0 K (205.2 K) observed in the heating (cooling) modes, respectively. Observed transitions involve a transformation from high-temperature orthorhombic phase I, with the centrosymmetric space group Pmmn, through the room-temperature modulated phase II, with the average structure being isostructural to I, to the low-temperature monoclinic phase III, with non-centrosymmetric space group P21. The intermediate phase II is a rare example of a modulated structure in 2D perovskites, with Pmmn(00γ)s00 superspace symmetry and modulation vector q ≅ 0.25c*. MHy2PbCl4 beats the previous record of MHy2PbBr4 in terms of the shortest inorganic interlayer distance in 2D perovskites (8.79 Å at 350 K vs 8.66 Å at 295 K, respectively). The characteristics of phase transitions are explored with differential scanning calorimetry, dielectric, and Raman spectroscopies. The non-centrosymmetry of phase III is confirmed with second harmonic generation (SHG) measurements, and polarity is demonstrated by the pyroelectric effect. MHy2PbCl4 also exhibits thermochromism, with the photoluminescence (PL) color changing from purplish-blue at 80 K to bluish-green at 230 K. The demonstration of polar characteristics for one more member of the methylhydrazinium perovskites settles a debate about whether this approach can present value for the crystal engineering of acentric solids similar to that which was recently adopted by a so-called fluorine substitution effect.