Novel bio-materials, like chitosan and its derivatives, appeal to finding a new niche in room temperature gas sensors, demonstrating not only a chemoresistive response, but also changes in mechanical impedance due to vapor adsorption. We determined the coefficients of elasticity and viscosity of chitosan acetate films in air, ammonia, and water vapors by acoustic spectroscopy. The measurements were carried out while using a resonator with a longitudinal electric field at the different concentrations of ammonia (100–1600 ppm) and air humidity (20–60%). It was established that, in the presence of ammonia, the longitudinal and shear elastic modules significantly decreased, whereas, in water vapor, they changed slightly. At that, the viscosity of the films increased greatly upon exposure to both vapors. We found that the film’s conductivity increased by two and one orders of magnitude, respectively, in ammonia and water vapors. The effect of analyzed vapors on the resonance properties of a piezoelectric resonator with a lateral electric field that was loaded by a chitosan film on its free side was also experimentally studied. In these vapors, the parallel resonance frequency and maximum value of the real part of the electrical impedance decreased, especially in ammonia. The results of a theoretical analysis of the resonance properties of such a sensor in the presence of vapors turned out to be in a good agreement with the experimental data. It has been also found that with a growth in the concentration of the studied vapors, a decrease in the elastic constants, and an increase in the viscosity factor and conductivity lead to reducing the parallel resonance frequency and the maximum value of the real part of the electric impedance of the piezoelectric resonator with a lateral electric field that was loaded with a chitosan film. This leads to an increase in the sensitivity of such a sensor during exposure to these gas vapors.