To fully achieve potential applications of the double-decker molecules containing rare earth elements as single-molecule magnets in molecular spintronics, it is crucial to understand the 4f states of the rare earth atoms sandwiched in the double-decker molecules by metal electrodes. In this study, low-temperature scanning tunneling microscopy and spectroscopy were employed to investigate the isolated double-decker DyPc2 molecule adsorbed on Au(111) via its differential conductance measurements. The experimental results revealed that the differential conductance maps acquired at a constant height mode simply depicted the authentic molecular orbitals; moreover, the differential conductance maps achieved at a constant current mode could not directly probe the 4f states of the sandwiched Dy atom. This was consistent with the spectra obtained over the molecule center around the Fermi level, indicative of no Kondo feature. Upon decreasing the tip-molecule distance, the CH-mode images presented high-resolution structure but no information of the 4f states. All results indicated that the Dy atom barely contributed to the tunneling current because of the absence of coupling with the microscope tip, echoing the inaccessibility of the Dy 4f states in the double-decker DyPc2 molecule.