In the present work, we construct eight six-quark currents to study the Σc Σc baryonium and ΣcΣc dibaryon states via the QCD sum rules. For either Σc Σc baryonium or ΣcΣc dibaryon states, we construct four currents with the J P = 1 − , 1 + , 0 + and 0 − . Except the current 1 + of ΣcΣc, we find the Borel windows for the other seven. There are two possible Σc Σc molecular states or compact six-quark states with the J P = 1 − and 0 − . The results of the current 0 + of ΣcΣc show a possible ΣcΣc molecular state with 20 MeV binding energy. We find two Σc Σc baryonium resonances states with the J P = 1 + , 0 + and two ΣcΣc dibaryon resonances states with the J P = 0 − , 1 − , respectively. Pole residues of the seven states are also calculated.