  We present an analysis using the MOSFIRE Deep Evolution Field (MOSDEF) survey
on the nature of "MIR-excess" galaxies, which have star formation rates (SFR)
inferred from mid-infrared (MIR) data that is substantially elevated relative
to that estimated from dust-corrected UV data. We use a sample of $\sim$200
galaxies and AGN at $1.40<z<2.61$ with 24 $\mu$m detections (rest-frame
8$\mu$m) from MIPS/\textit{Spitzer}. We find that the identification of
MIR-excess galaxies strongly depends on the methodologies used to estimate IR
luminosity ($\rm L_{IR}$) and to correct the UV light for dust attenuation. We
find that extrapolations of the SFR from the observed 24 $\mu$m flux, using
luminosity-dependent templates based on local galaxies, substantially
overestimate $\rm L_{IR}$ in $z\sim2$ galaxies. By including \textit{Herschel}
observations and using a stellar mass-dependent, luminosity-independent $\rm
L_{IR}$, we obtain more reliable estimates of the SFR and a lower fraction of
MIR-excess galaxies. Once stellar mass selection biases are taken into account,
we identify $\sim24\%$ of our galaxies as MIR-excess. However, $\rm
SFR_{H\alpha}$ is not elevated in MIR-excess galaxies compared to MIR-normal
galaxies, indicating that the intrinsic fraction of MIR-excess may be lower.
Using X-ray, IR, and optically-selected AGN in MOSDEF, we do not find a higher
prevalence for AGN in MIR-excess galaxies relative to MIR-normal galaxies. A
stacking analysis of X-ray undetected galaxies does not reveal a harder
spectrum in MIR-excess galaxies relative to MIR-normal galaxies. Our analysis
indicates that AGN activity does not contribute substantially to the MIR excess
and instead implies that it is likely due to the enhanced PAH emission.
