The collisional dependence of polarization spectroscopy (PS) with a picosecond-pulse laser is investigated theoretically with a perturbative treatment and experimentally by probing hydroxyl (OH) in a flow cell with a buffer gas of argon. Using a frequency-doubled distributed-feedback dye laser (DFDL), the PS signal strength is monitored as a function of pressure using a nonsaturating pump beam and a saturating pump beam. The collisional dependence of the PS signal is found to decrease significantly with a saturating pump beam. Increasing the flow-cell pressure by a factor of 50 (from 10 torr to 500 torr), the PS signal strength produced with a nonsaturating pump beam decreases by a factor of 18 while that produced with a saturating pump decreases by only a factor of 3. A third-order perturbative (weak-field) approach is used to develop an analytical expression for the PS signal generated by single-mode, exponentially decaying laser pulses. This expression correctly predicts the experimental results acquired with the nonsaturating pump beam. The analytical solution is used to examine the effects of pulse length on the collisional dependence of the weak-field PS signal strength. Results are also presented for a numerical simulation of the time-dependent density matrix equations for the high intensity case.