Parity of spin states

Since orbital angular momentum commutes with the parity operator and since both are hermitian it is possible to build a common basis. These are the spherical harmonics, whose parity is known.

Now, we also know that since the spin operator commutes with the parity operator we can build common eigenkets, but I have never been told which is the parity of a spin state.

Moreover, when calculating the parity of, for example, a particle I always multiply the contribution of the orbital angular momentum by the intrinsic parity of the particle, and the spin part is never mentioned.

I guess that the spin contribution is in that intrinsic parity. So i would like someone to tell me about the parity of the spin states and how they are related to the intrinsic parity of particles(if in fact my guess is right)