  We analyse the power spectrum of the Baryon Oscillation Spectroscopic Survey
(BOSS), Data Release 12 (DR12) to constrain the relative velocity effect, which
represents a potential systematic for measurements of the Baryon Acoustic
Oscillation (BAO) scale. The relative velocity effect is sourced by the
different evolution of baryon and cold dark matter perturbations before
decoupling. Our power spectrum model includes all $1$-loop redshift-space terms
corresponding to $v_{\rm bc}$ parameterised by the bias parameter $b_{v^2}$. We
also include the linear terms proportional to the relative density,
$\delta_{\rm bc}$, and relative velocity dispersion, $\theta_{\rm bc}$, which
we parameterise with the bias parameters $b^{\rm bc}_{\delta}$ and $b^{\rm
bc}_{\theta}$. Our data does not support a detection of the relative velocity
effect in any of these parameters. Combining the low and high redshift bins of
BOSS, we find limits of $b_{v^2} = 0.012 \pm 0.015\;(\pm 0.031)$, $b^{\rm
bc}_{\delta} = -1.0 \pm 2.5\;(\pm 6.2)$ and $b^{\rm bc}_{\theta} = -114 \pm
55\;(\pm 175)$ with $68\%$ ($95\%$) confidence levels. These constraints
restrict the potential systematic shift in $D_A(z)$, $H(z)$ and $f\sigma_8$,
due to the relative velocity, to $1\%$, $0.8\%$ and $2\%$, respectively. Given
the current uncertainties on the BAO measurements of BOSS these shifts
correspond to $0.53\sigma$, $0.5\sigma$ and $0.22\sigma$ for $D_A(z)$, $H(z)$
and $f\sigma_8$, respectively.
