  In this paper, we explore the behavior of optical polarization during the
multi-wavelength outburst of the blazar Mrk 421 detected in February 2010. We
use optical polarization measurements in the wavelength range 500-700 nm from
SPOL observations available between January 1, 2010 and March 31, 2010 (MJD
55197-55286) including the period of multi-wavelength flaring activity detected
from the source around February 16-17, 2010 (MJD 55243-55244). We also use near
simultaneous optical and radio flux measurements from SPOL in V and R bands and
OVRO at 15 GHz respectively. We find that the emissions in the optical and
radio bands do not show any significant change in the source activity unlike at
X-ray and $\gamma$--ray energies during the outburst. The optical and radio
flux measurements are found to be consistent with the long term quiescent state
emission of the source. Moreover, the linear polarization in the wavelength
range 500-700 nm decreases to a minimum value of 1.6$\%$ during the X-ray and
$\gamma$--ray outburst which is significantly lower than the long term average
value of $\sim$ 4.2$\%$. The angle of polarization varies between
114$^\circ$-163$^\circ$ with a preferred average value of $\sim$ 137$^\circ$
during this period. We estimate the degree of polarization intrinsic to the jet
taking into account the host galaxy contamination in R band and compare this
with the theoretical synchrotron polarization estimated for a power law
distribution of relativistic electrons gyrating in an emission region filled
with ordered and chaotic magnetic fields. The intrinsic linear polarization
estimated for different epochs during the above period is found to be
consistent with the theoretical synchrotron polarization produced by the
relativistic electrons with power law spectral index $\sim$ 2.2.
