The effects of optically turbid medium on polarization states of incident light are studied using a novel linear Stokes polarimeter. The optical rotation and surviving linear polarization fraction of light scattered from highly turbid media (scattering coefficient μs = 100 cm-1) are measured both in and off the incident plane while the detection angle changes from forward direction (0°) to backward directions (135°, 145° and 155°). The response of the optical rotation and surviving linear polarization to the presence of glucose molecules (0.06M - 0.9M) is also studied. The results show that in the absence of glucose, the scattering-induced optical rotation is zero in the incident plane for all detection angles, and increases with detection angle when measured off the incident plane. Conversely, the surviving linear polarization fraction increases with detection angle in the incident plane, and decreases when off the incident plane. Thus, when measured in the incident plane, optical rotation is least sensitive to glucose in the turbid medium, whereas the surviving linear polarization is most sensitive. For the above turbidity and glucose concentration ranges, the optimal glucose detection sensitivity using optical rotation is at 135° detection angle, 2 mm off the incident plane, while it is at 135° detection angle in the incident plane if surviving linear polarization is used as a glucose probe. This work demonstrates the complexity of polarimetry in turbid chiral media and underscores the importance of detection geometry in making and interpreting turbid polarimetry measurements.