The local superfluid density around a molecule embedded in a He-4(N) cluste
r at low temperatures is analyzed using the path-integral Monte Carlo metho
d. The molecular interaction induces a local nonsuperfluid component within
a quantum solvation shell whose size is determined by the range of the mol
ecule-helium interaction, and also introduces an anisotropic layering of th
e superfluid density around the molecule. We show that a local quantum hydr
odynamic analysis is internally consistent for N > 50, and can be used to c
alculate effective rotational constants for molecular dopants in superfluid
helium.