The decay of the Ricci-flat Kähler form $\omega_{TY}$ to its asymptotic model $\omega_{\mathcal{C}}$ is weaker than the decay of the complex structure and of the holomorphic volume form. The reason is that the latter is obtained by an explicit computation where the errors admit an expansion in terms of $|w|\sim e^{-z^{n}/2}$. On the other hand, the decay rate of $\omega_{TY}$ depends on an analysis of the Tian-Yau solution of the Monge-Ampère equation, which is related to the fact that the decay rate of harmonic (not necessarily holomorphic) functions on the Calabi model space (see Section 4) is in general only $O(e^{-\delta z^{n/2}})$. It is an interesting question if $O(e^{-\delta z^{n/2}})$ decay of the Kähler form is indeed optimal. This is a global question because one can easily construct Tian-Yau solutions outside a compact set with leading term equal to any given decaying harmonic function which is not pluriharmonic.