Nonclassical response and acoustic resonance of a torsional oscillator (TO) containing solid helium is investigated under dc rotation. Acoustic resonance measurements can capture the elastic property of solid helium in the annular channel where we simultaneously measure the torsional oscillator response. Superposition of dc rotation on top of two resonance measurements can clarify whether or not the reduction in the resonant period of the TO is originated from the elastic property of solid helium more clearly. We find that the acoustic resonance is independent of dc rotation. On the contrary, the TO response measured simultaneously shows strong suppression which was accompanied by additional dissipation of the TO. This study supports the existence of a macroscopically phase coherent superfluid state in solid helium.