Gas and star velocity dispersions have been derived for eight circumnuclear star-forming regions (CNSFRs) and the nucleus of the spiral galaxy NGC 3310 using high-resolution spectroscopy in the blue and far red. Stellar velocity dispersions have been obtained from the Ca ii triplet in the near-IR, using cross-correlation techniques, while gas velocity dispersions have been measured by Gaussian fits to the Hβ λ4861 Å and [O iii] λ5007 Å emission lines.The CNSFR stellar velocity dispersions range from 31 to 73 km s-1. These values, together with the sizes measured on archival Hubble Space Telescope images, yield upper limits to the dynamical masses for the individual star clusters between 1.8 and 7.1 × 106 M⊙, for the whole CNSFR between 2 × 107 and 1.4 × 108 M⊙, and 5.3 × 107 M⊙, for the nucleus inside the inner 14.2 pc. The masses of the ionizing stellar population responsible for the H ii region gaseous emission have been derived from their published Hα luminosities and are found to be between 8.7 × 105 and 2.1 × 106 M⊙ for the star-forming regions and 2.1 × 105 M⊙ for the galaxy nucleus; they therefore constitute between 1 and 7 per cent of the total dynamical mass.The ionized gas kinematics is complex; two different kinematical components seem to be present as evidenced by different linewidths and Doppler shifts.