  Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal
reduced-order modeling of non-parametric linear time-invariant (LTI) systems
are known and well-investigated. In this work, using the general framework of
$\mathcal{L}_2$-optimal reduced-order modeling of parametric stationary
problems, we derive interpolatory $\mathcal{H}_2 \otimes
\mathcal{L}_2$-optimality conditions for parametric LTI systems with a general
pole-residue form. We then specialize this result to recover known conditions
for systems with parameter-independent poles and develop new conditions for a
certain class of systems with parameter-dependent poles.
