Optical imaging of objects embedded within scattering media such as biological tissues suffers from the loss of resolving power. In our previous work, we proposed an approach called collective accumulation of single scattering (CASS) microscopy that attenuates this detrimental effect of multiple light scattering by combining the time-gated detection and spatial input-output correlation. In the present work, we perform a rigorous theoretical analysis on the effect of multiple light scattering to the optical transfer function of CASS microscopy. In particular, the spatial frequency-dependent signal to noise ratio (SNR) is derived depending on the intensity ratio of the single- and multiple-scattered waves. This allows us to determine the depth-dependent resolving power. We conducted experiments using a Siemens star-like target having various spatial frequency components and supported the theoretical derived SNR spectra. Our study provides a theoretical framework for understanding the effect of multiple light scattering in high-resolution and deep-tissue optical imaging.