Recent theoretical and observational works indicate the presence of a correlation between the star-formation rate (SFR) and active galactic nucleus (AGN) luminosity (and, therefore, the black hole accretion rate, \dot{M}_BH) of Seyfert galaxies. This suggests a physical connection between the gas-forming stars on kpc scales and the gas on sub-pc scales that is feeding the black hole. We compiled the largest sample of Seyfert galaxies to date with high angular resolution (~0.''4-0.''8) mid-infrared (8-13 μm) spectroscopy. The sample includes 29 Seyfert galaxies drawn from the AGN Revised Shapley-Ames catalog. At a median distance of 33 Mpc, our data allow us to probe nuclear regions on scales of ~65 pc (median value). We found no general evidence of suppression of the 11.3 μm polycyclic aromatic hydrocarbon (PAH) emission in the vicinity of these AGN, and we used this feature as a proxy for the SFR. We detected the 11.3 μm PAH feature in the nuclear spectra of 45% of our sample. The derived nuclear SFRs are, on average, five times lower than those measured in circumnuclear regions of 600 pc in size (median value). However, the projected nuclear SFR densities (median value of 22 M ☉ yr–1 kpc–2) are a factor of 20 higher than those measured on circumnuclear scales. This indicates that the SF activity per unit area in the central ~65 pc region of Seyfert galaxies is much higher than at larger distances from their nuclei. We studied the connection between the nuclear SFR and \dot{M}_BH and showed that numerical simulations reproduce our observed relation fairly well.