We investigated the correlations among the structure, Rayleigh scattering, and single-molecule surface-enhanced Raman scattering (SERS) of DNA-tethered Au-Ag core-shell nanoparticles, especially in dimer and trimer forms. For the optimal correlation measurements, accurate information on the position of the nanoparticle is crucial for locating the nanoparticle at the center of the excitation source for the optical measurements. To achieve this, we developed a multistep correlation strategy that enables us to unambiguously correlate the AFM images with optical images within a few nanometers. We also newly defined the correlation accuracy in this paper as a useful concept for the correlation measurements. With this reliable correlation accuracy, we performed various statistical analyses to thoroughly elucidate the relationships between particle structure, Rayleigh scattering and SERS in terms of the incident polarization and scattering intensity ratio.