An apparatus and method of making a hole of a first predetermined diameter in a dura of a patient for the insertion of a catheter having a second predetermined diameter. A burr hole is created in the cranium of the patient, if necessary. A stylet is inserted into the lumen of a catheter with an end of the stylet formed with a tip having a diameter having a predetermined relationship with the first predetermined diameter such that the distal end of the stylet is proximate to a distal end of the catheter. The end of the catheter is inserted into the burr hole of the cranium. An electrical current is applied to the stylet in order to cauterize the dura creating a hole in the dura approximately equal to the diameter of the tip.