We present a combined differential scanning calorimetry (DSC) and infrared (IR), Raman, electron paramagnetic resonance (EPR), and NMR spectroscopy study of dimethylammonium zinc formate frameworks [(CH3)2NH2][Zn(HCOO)3] containing 14N and 15N nitrogen isotopes. The DSC reveals very small differences in the phase-transition temperatures for both compounds. The IR and Raman spectroscopies indicate different frequencies of the vibrational modes that involve a nitrogen atom. The temperature-dependent IR and Raman spectra also show a tiny isotope effect on the properties and temperature of the phase transition. The EPR measurements are performed for both compounds doped with small amount of paramagnetic Mn2+ ions. The obtained continuous-wave Mn2+ EPR spectra of the disordered phase are very similar for both frameworks, whereas the temperature dependence of the zero-field splitting parameter indicates a slightly different distortion of the MnO6 octahedra in the low-temperature phase. The EPR line width analys...