Local luminous infrared ( IR ) galaxies ( LIRGs ) have both high star formation rates ( SFR ) and a high AGN ( Seyfert and AGN/starburst composite ) incidence . Therefore , they are ideal candidates to explore the co-evolution of black hole ( BH ) growth and star formation ( SF ) activity , not necessarily associated with major mergers . Here , we use Spitzer /IRS spectroscopy of a complete volume-limited sample of local LIRGs ( distances of < 78 Mpc ) . We estimate typical BH masses of 3 \times 10 ^ { 7 } M _ { \odot } using [ Ne iii ] 15.56 \mu m and optical [ O iii ] \lambda 5007 gas velocity dispersions and literature stellar velocity dispersions . We find that in a large fraction of local LIRGs the current SFR is taking place not only in the inner nuclear \sim 1.5 kpc region , as estimated from the nuclear 11.3 \mu m PAH luminosities , but also in the host galaxy . We next use the ratios between the SFRs and BH accretion rates ( BHAR ) to study whether the SF activity and BH growth are contemporaneous in local LIRGs . On average , local LIRGs have SFR to BHAR ratios higher than those of optically selected Seyferts of similar AGN luminosities . However , the majority of the IR-bright galaxies in the RSA Seyfert sample behave like local LIRGs . Moreover , the AGN incidence tends to be higher in local LIRGs with the lowest SFRs . All this suggests that in local LIRGs there is a distinct IR-bright star forming phase taking place prior to the bulk of the current BH growth ( i.e. , AGN phase ) . The latter is reflected first as a composite and then as a Seyfert , and later as a non-LIRG optically identified Seyfert nucleus with moderate SF in its host galaxy .