  We compute general expressions for two types of three-point functions of
(semi-)short multiplets in four-dimensional $\mathcal{N}=2$ superconformal
field theories. These (semi-)short multiplets are called "Schur multiplets" and
play an important role in the study of associated chiral algebras. The first
type of the three-point functions we compute involves two half-BPS Schur
multiplets and an arbitrary Schur multiplet, while the second type involves one
stress tensor multiplet and two arbitrary Schur multiplets. From these
three-point functions, we read off the corresponding OPE selection rules for
the Schur multiplets. Our results particularly imply that there are non-trivial
selection rules on the quantum numbers of Schur operators in these multiplets.
We also give a conjecture on the selection rules for general Schur multiplets.
