  We study the evidence for a connection between active galactic nuclei (AGN)
fueling and star formation by investigating the relationship between the X-ray
luminosities of AGN and the star formation rates (SFRs) of their host galaxies.
We identify a sample of 309 AGN with $10^{41}<L_\mathrm{X}<10^{44} $ erg
s$^{-1}$ at $0.2 < z < 1.2$ in the PRIMUS redshift survey. We find AGN in
galaxies with a wide range of SFR at a given $L_X$. We do not find a
significant correlation between SFR and the observed instantaneous $L_X$ for
star forming AGN host galaxies. However, there is a weak but significant
correlation between the mean $L_\mathrm{X}$ and SFR of detected AGN in star
forming galaxies, which likely reflects that $L_\mathrm{X}$ varies on shorter
timescales than SFR. We find no correlation between stellar mass and
$L_\mathrm{X}$ within the AGN population. Within both populations of star
forming and quiescent galaxies, we find a similar power-law distribution in the
probability of hosting an AGN as a function of specific accretion rate.
Furthermore, at a given stellar mass, we find a star forming galaxy $\sim2-3$
more likely than a quiescent galaxy to host an AGN of a given specific
accretion rate. The probability of a galaxy hosting an AGN is constant across
the main sequence of star formation. These results indicate that there is an
underlying connection between star formation and the presence of AGN, but AGN
are often hosted by quiescent galaxies.
