We study the local and nonlocal charge transport properties of three-terminal nanostructure, consisting of the correlated quantum dot embedded between two metallic electrodes and superconductor. Using the linear response theory, we analyze interplay of the induced on-dot pairing with the correlation effects, inspecting their influence on the conductance and thermopower. Our calculations predict negative values of the nonlocal conductance and reversal of the Seebeck coefficient when the quantum dot ground state is represented by the BCS-type singlet configuration. These phenomena are realized when the subgap charge transport is predominantly contributed by the crossed Andreev scattering. In contrast, on the doublet side, we obtain signatures for the Kondo effect manifested by the low-temperature enhancement of the charge conductance and clearly evident in the thermopower. Such temperature-dependent local and nonlocal transport properties can unambiguously identify the specific configuration of the correlated quantum dot and reveal the rich physics emerging in the doublet-to-singlet crossover region.