In the present work, the partial decay widths of Pc(4312) to ηcp and J/ψp are investigated with the QCD sum rule method under the assumption that Pc(4312) is a DΣc molecular state with JP = 1/2−. In the analysis, the pole residue of Pc(4312), one of the input parameters for the calculations of the strong decay constants, is calculated first. With the numerical values of the strong decay constants, the partial decay widths to ηcp and J/ψp are estimated to be Γ(Pc(4312) → ηcp) = 5.54+0.75−0.5 MeV and Γ(Pc(4312) → J/ψp) = 1.6 7+0.92−0.56 MeV, respectively, which are compatible with the measured total width of Pc(4312). The results suggest that it is reasonable to assign Pc(4312) to be a DΣc molecular state with JP = 1/2−.