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The study of the Canonical Forms of the Killing Tensor concerns thesimultaneous resolving of the Integrability Conditions of the Killing Tensoralong with the Einstein's Field Equations employing the framework ofNewman-Penrose Formalism. We present all the Petrov Types admitting the 2nd and3rd Canonical Forms of Killing Tensor in Vacuum in the frame of General Theoryof Relativity. During the investigation of the Type D solution of 2nd Canonicalform of the Killing Tensor the Carter's Case [D] solution in Vacuum emerged.

Carter's case [D] admits the 2nd Canonical Form of the Killing Tensor