We have carried out an analysis of the radio and optical properties of a statistical sample of 45 Seyfert galaxies from the Palomar spectroscopic survey of nearby galaxies . We find that the space density of bright galaxies ( -22 mag \leq M _ { B _ { T } } \leq - 18 mag ) showing Seyfert activity is ( 1.25 \pm 0.38 ) \times 10 ^ { -3 } Mpc ^ { -3 } , considerably higher than found in other Seyfert samples . Host galaxy types , radio spectra , and radio source sizes are uncorrelated with Seyfert type , as predicted by the unified schemes for active galaxies . Approximately half of the detected galaxies have flat or inverted radio spectra , more than expected based on previous samples . Surprisingly , Seyfert 1 galaxies are found to have somewhat stronger radio sources than Seyfert 2 galaxies at 6 and 20 cm , particularly among the galaxies with the weakest nuclear activity . We suggest that this difference can be accommodated in the unified schemes if a minimum level of Seyfert activity is required for a radio source to emerge from the vicinity of the active nucleus . Below this level , Seyfert radio sources might be suppressed by free-free absorption associated with the nuclear torus or a compact narrow-line region , thus accounting for both the weakness of the radio emission and the preponderance of flat spectra . Alternatively , the flat spectra and weak radio sources might indicate that the weak active nuclei are fed by advection-dominated accretion disks .