Contact resonance atomic force microscopy (CR-AFM) is a powerful technique that enables the measurement of topography and the mechanical properties of various materials at the micro/nanoscale. It can be used in both air and liquid environments. However, when CR-AFM is operated in a liquid environment, the dynamic behaviors of the microcantilever can be significantly different from those in air or vacuum due to the complex fluid-solid coupling of the microcantilever-liquid-sample system and the tip-sample interaction. In this study, we explore the effects of liquid density and viscosity, as well as tip-sample normalized contact stiffness and contact damping, on the dynamics of the AFM microcantilever in liquid environments. We treat the influence of the liquid on the dynamics of the AFM microcantilever as added mass and added damping. Our results show that in free vibration, the natural frequencies of the AFM microcantilever are primarily dominated by the liquid density, while the liquid viscosity plays a dominant role in the quality factor compared to the liquid density. Higher modes exhibit higher sensitivity to changes in liquid viscosity and liquid density. As the normalized tip-sample contact stiffness increases, a higher mode shows increased sensitivity to changes in normalized contact stiffness in a liquid environment. On the other hand, a lower mode is more sensitive to changes in normalized contact damping in a liquid environment. In addition, the dynamic responses of the AFM microcantilever under three different excitation approaches are compared and discussed. Variations in boundary conditions and hydrodynamic loads applied to the microcantilever under these approaches lead to diverse dynamic responses. The findings in this study are essential for the development of micro/nanoscale mechanical property imaging techniques using CR-AFM in liquid environments, as well as the improvement of measurement accuracy and sensitivity.