Level lifetimes in the 32 P nucleus have been determined using the Doppler Shift Attenuation Method (DSAM). Conventional DSAM measurements employ a thin target on a thick, high Z backing. An extension of the technique to thick molecular targets is presented. The necessary modifications in the standard analysis procedures, pertaining to the incorporation of stopping power estimations for molecular media and evolution of residue cross-section in thick target, have been implemented. Further, x-ray powder diffraction (XRD) and scanning electron-microscopy (SEM) have also been carried out to probe the structural composition of the target. The lifetime results have been validated with respect to the previous measurements and upper limit on lifetimes of seven levels have been determined for the first time. Large basis shell model calculations have been carried out and compared with the experimental measurements.