An obturator sleeve for a trocar assembly and method of its use are disclosed for infiltrating a liquid medication such as a local anesthetic into the tissue walls of a port site wound during a laparoscopic procedure. The sleeve includes an internal flow passage for receiving the liquid medication. A diffusion polymer, located within the internal flow passage, first absorbs the liquid medication and then releases the liquid medication through a plurality of apertures in the sleeve. When port site wound tissue contacts the diffusion polymer, the diffusion polymer within the sleeve steadily releases the absorbed medication through the plurality of apertures. The obturator sleeve provides a means to adequately infiltrate medication into the tissues of the port site wound, and can be used to block the free nerve endings of the port site wound as well as nearby sensory and motor nerves.