Since you used some specific words in your question, I will respond a certain way. Cracks are generated by mechanical action, and cannot be machined in. They may, in certain brittle materials, be a byproduct of machining.
Using a method like EDM will alter the properties of a polymer nearby, as it will heat the polymer. If you are interested in introducing a crack for the purposes of fracture testing (see the reference to ASTM D5045 below), then it is imperative that you create a "sharp" crack that is representative of the material (and thus EDM is not a good choice). The method for doing this involves machining a notch in the plastic at the test zone, and then using mechanical load to precrack the specimen. The precrack needs to be measured, and then the fracture testing can commence.
If, when you said "crack" what you actually meant was that you need to cut a small opening in the polymeric material, I suggest you change your wording to "machine a hole or slit". In that case, I suggest a CNC end mill with a very small diameter bit, which will achieve tolerances approaching an EDM wire. If kept cool enough, this will not alter the local properties of the polymer. If this is not fine enough, then you are most certainly in need of a CNC laser cutter, which again will locally alter the material.
For method reference, see ASTM D5045-14: Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials
General information about material fracture: https://en.wikipedia.org/wiki/Fracture
EDIT: Now that you have posted the drawing, I suggest an end mill. Bits are readily available that will machine that, particularly if it is not a hard material. You will want to work with a machine shop that does precision machining, and ask them specifically about tolerances. Also, I suggest you have them cut some samples prior to fabricating the final article so you can evaluate their tolerances.