The gamma-ray blazar OJ 287 was in a high activity state during December 2015 - February 2016. Coinciding with this high brightness state, we observed this source for photometry on 40 nights in R-band and for polarimetry on 9 epochs in UBVRI bands. During the period of our observations, the source brightness varied between $13.20 pm 0.04$ to $14.98 pm 0.04$ mag and the degree of polarization (P ) fluctuated between $6.0 pm 0.3$% and $28.3 pm 0.8$% in R-band. Focusing on intra-night optical variability (INOV), we find a duty cycle of about 71% using $chi^2$-statistics, similar to that known for blazars. From INOV data, the shortest variability time scale is estimated to be $142 pm 38$ min yielding a lower limit of the observed Doppler factor $delta_0 = 1.17$, the magnetic field strength $B le 3.8$ G and the size of the emitting region Rs < $2.28 times 10^{14}$ cm. On inter-night timescales, a significant anti-correlation between R-band flux and P is found. The observed P at U-band is generally larger than that observed at longer wavelength bands suggesting a wavelength dependent polarization. Using V -band photometric and polarimetric data from Steward Observatory obtained during our monitoring period we find a varied correlation between P and V-band brightness. While an anticorrelation is seen between P and V -band mag at sometimes, no correlation is seen at other times, thereby, suggesting the presence of more than one short-lived shock components in the jet of OJ 287.
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