yes it is. it is a theorem that all quantum field theories that satisfy relatively weak conditions (locality, unitarity, S-matrix,...) are CPT-invariant. weak interactions are no exception. you can prove it by referring to that theorem, or by just brute-force transforming the action under CPT and seeing that it's invariant.
Proof of the CPT theorem is nontrivial and requires quite a bit of background. But it is a deep and important mathematical truism about quantum field theories.
There are various books that treat it in varying degrees of rigor. I think Weinberg proves it in his volumes, and for a more mathematical treatment see Streeter/Wightman.
Incidentally people look for violation of the CPT experimentally, so far without success. But it would be a big deal if one day such a fundamental symmetry was broken. It would mean probably that we would need to go back to Constructive field theories for insight.