This is a catheter assembly designed for accessing the cerebrospinal fluid circulation system and draining fluid therefrom. The polymeric thin-walled catheter has a soft, flexible distal region for minimizing trauma to tissue and angularly accessing the subarachnoid space in the cerebrospinal fluid pathway with an optional guidewire. A stiffer proximal region, which may optionally contain a reinforcing woven braid or coil ensures that the catheter does not kink or compress during use in the tough membranes around the spinal column. One or more apertures in the catheter wall for draining fluid proximally through the catheter central lumen allows for transport of fluid through the catheter at therapeutic flow rates and pressures. A soft polymeric plug that may be disposed in the distal end of the catheter assembly ensure minimal trauma to tissue upon entry. The entire catheter may be coated with hydrophilic coating to facilitate movement through an optional Touhy needle and tissue, and may be radio-opaque for greater visibility under fluoroscopy.