We present estimates of black hole accretion rates and nuclear, extended, and total star-formation rates for a complete sample of Seyfert galaxies. Using data from the Spitzer Space Telescope, we measure the active galactic nucleus (AGN) luminosity using the [O IV] 25.89 micron emission line and the star-forming luminosity using the 11.3 micron aromatic feature and extended 24 micron continuum emission. We find that black hole growth is strongly correlated with nuclear (r<1 kpc) star formation, but only weakly correlated with extended (r>1 kpc) star formation in the host galaxy. In particular, the nuclear star-formation rate (SFR) traced by the 11.3 micron aromatic feature follows a relationship with the black hole accretion rate (BHAR) of the form SFRproptoBHAR^0.8, with an observed scatter of 0.5 dex. This SFR-BHAR relationship persists when additional star formation in physically matched r=1 kpc apertures is included, taking the form SFRproptoBHAR^0.6. However, the relationship becomes almost indiscernible when total SFRs are considered. This suggests a physical connection between the gas on sub-kpc and sub-pc scales in local Seyfert galaxies that is not related to external processes in the host galaxy. It also suggests that the observed scaling between star formation and black hole growth for samples of AGNs will depend on whether the star formation is dominated by a nuclear or extended component. We estimate the integrated black hole and bulge growth that occurs in these galaxies and find that an AGN duty cycle of 5-10% would maintain the ratio between black hole and bulge masses seen in the local universe.
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