The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the $N$-extended superparticle is shown to be anomalous when $N$ is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral $U(1)$ gauge invariance. This accords with the fact that no massless $N$=1 super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when $N$ is even, but it has $2$ states when $12$$N$ is odd (e.g. the $N$=2 hypermultiplet) in contrast to just $2$ when $12$$N$ is even (e.g. the $N$=4 Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when $12$$N$ is odd.