Morphology-dependent resonances (MDRs) for a coated spherical particle are important because of their extensive applications. However, MDRs for coated spherical particles are more complicated than those for homogeneous particles. In this paper, a general expression is proposed for calculating the scattering efficiency of a specific layer of coated particle. Reformulations of internal scattering efficiency are made, which provides a new, to the best of our knowledge, method to investigate the resonance in the core and in the shell independently. MDRs in the core can be shown in four cases on the outmost scattering efficiency curve. To investigate the reason of the resonance, the relationships between MDRs in the core, outmost scattering efficiency, and partial wave are analyzed. It is numerically shown that the expressions are reliable and efficient, which provides a theoretical fundamental for studying of resonances of multilayered particles and for measurement.