The best way to get wadded up tape apart so it can be processed for latent prints on either the smooth or adhesive side is to place it in a freezer for 24 hours, use dry ice or liquid nitrogen. This will cause the adhesive to release and the tape can be pulled apart. Another method to try is the use of Component Spray. When sprayed on, the tape will freeze to approximately 65 degrees in an instant. You control the area you are working on. Hold the tape with hemostats but not with your fingers. Attach the small tube that comes with the component spray and spray the tape to get it cold. Start pulling the tape apart to open it up. If the tape resists coming apart, use more component spray. Either side can now be processed.
Component spray can be purchased at Radio Shack and retails for approximately $6.95.