The physical properties of the organic-inorganic hybrid crystals having the formula [NH3(CH2)3NH3]ZnX4 (X = Cl, Br) were investigated. The phase transition temperatures (TC; 268K for Cl and 272K for Br) of the two crystals bearing different halogen atoms in their skeletons were determined through differential scanning calorimetry. The thermodynamic properties of the two crystals were investigated through thermogravimetric analysis. The structural dynamics, particularly the role of the [NH3(CH2)3NH3] cation, were probed through 1H and 13C magic-angle spinning nuclear magnetic resonance spectroscopy as a function of temperature. The 1H and 13C NMR chemical shifts did not show any changes near TC. In addition, the 1H spin-lattice relaxation time (T1ρ) varied with temperature, whereas the 13C T1ρ values remained nearly constant at different temperatures. The T1ρ values of the atoms in [NH3(CH2)3NH3]ZnCl4 were higher than those in [NH3(CH2)3NH3]ZnBr4. The observed differences in the structural dynamics obtained from the chemical shifts and T1ρ values of the two compounds can be attributed to the differences in the bond lengths and halogen atoms. These findings can provide important insights or potential applications of these crystals.