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 U BV RI bands. During the period of our observations, the source brightness varied between 13.20 ± 0.04 to 14.98 ± 0.04 mag and the degree of polarization (P ) fluctuated between 6.0 ± 0.3% and 28.3 ± 0.8% in R-band. Focusing on intra-night optical variability (INOV), we find a duty cycle of about 71% using χ 2 -statistics, similar to that known for blazars. From INOV data, the shortest variability time scale is estimated to be 142 ± 38 min yielding a lower limit of the observed Doppler factor δ 0 = 1.17, the magnetic field strength B ≤ 3.8 G and the size of the emitting region R s < 2.28 × 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.