  We present the results of a spectroscopic analysis of rotational velocities
in 714 M dwarf stars observed by the SDSS III Apache Point Galactic Evolution
Experiment (APOGEE) survey. We use a template fitting technique to estimate
$v\sin{i}$ while simultaneously estimating $\log{g}$, $[\text{M}/\text{H}]$,
and $T_{\text{eff}}$. We conservatively estimate that our detection limit is 8
km s$^{-1}$. We compare our results to M dwarf rotation studies in the
literature based on both spectroscopic and photometric measurements. Like other
authors, we find an increase in the fraction of rapid rotators with decreasing
stellar temperature, exemplified by a sharp increase in rotation near the M$4$
transition to fully convective stellar interiors, which is consistent with the
hypothesis that fully convective stars are unable to shed angular momentum as
efficiently as those with radiative cores. We compare a sample of targets
observed both by APOGEE and the MEarth transiting planet survey and find no
cases were the measured $v\sin{i}$ and rotation period are physically
inconsistent, requiring $\sin{i}>1$. We compare our spectroscopic results to
the fraction of rotators inferred from photometric surveys and find that while
the results are broadly consistent, the photometric surveys exhibit a smaller
fraction of rotators beyond the M$4$ transition by a factor of $\sim 2$. We
discuss possible reasons for this discrepancy. Given our detection limit, our
results are consistent with a bi-modal distribution in rotation that is seen in
photometric surveys.
