We present new observations of HCN and HCO ^ { + } in the circumnuclear disk ( CND ) of the Galaxy , obtained with the APEX telescope . We have mapped emission in rotational lines of HCN J = 3–2 , 4–3 , and 8–7 , as well as HCO ^ { + } J = 3–2 , 4–3 , and 9–8 . We also present spectra of H ^ { 13 } CN J = 3–2 and 4–3 , and H ^ { 13 } CO ^ { + } J = 3–2 and 4–3 toward four positions in the CND . Using the intensities of all of these lines , we present an excitation analysis for each molecule using the non-LTE radiative transfer code RADEX . The HCN line intensities toward the northern emission peak of the CND yield log densities ( cm ^ { -3 } ) of 5.6 ^ { +0.6 } _ { -0.6 } , consistent with those measured with HCO ^ { + } as well as with densities recently reported for this region from an excitation analysis of highly-excited lines of CO . These densities are too low for the gas to be tidally stable . The HCN line intensities toward the CND ’ s southern emission peak yield log densities of 6.5 ^ { +0.5 } _ { -0.7 } , higher than densities determined for this part of the CND with CO ( although the densities measured with HCO ^ { + } , log [ n ] = 5.6 ^ { +0.2 } _ { -0.2 } , are more consistent with the CO-derived densities ) . We investigate whether the higher densities we infer from HCN are affected by mid-infrared radiative excitation of this molecule through its 14 \mu m rovibrational transitions . We find that radiative excitation is important for at least one clump in the CND , where we additionally detect the J = 4–3 , v _ { 2 } = 1 vibrationally-excited transition of HCN , which is excited by dust temperatures of \gtrsim 125-150 K. If this hot dust is present elsewhere in the CND , it could lower our inferred densities , potentially bringing the HCN-derived densities for the Southern part of the CND into agreement with those measured using HCO ^ { + } and CO. Additional sensitive , high-resolution submillimeter observations , as well as mid-infrared observations , would be useful to assess the importance of the radiative excitation of HCN in this environment .