In this note we show that an unbounded regular operator $t$ on Hilbert $C^*$-modules over an arbitrary $C^*$ algebra $ \mathcal{ A}$ has polar decomposition if and only if the closures of the ranges of $t$ and $|t|$ are orthogonally complemented, if and only if the operators $t$ and $t^*$ have unbounded regular generalized inverses. For a given $C^*$-algebra $ \mathcal{ A}$ any densely defined $\mathcal A$-linear closed operator $t$ between Hilbert $C^*$-modules has polar decomposition, if and only if any densely defined $\mathcal A$-linear closed operator $t$ between Hilbert $C^*$-modules has generalized inverse, if and only if $\mathcal A$ is a $C^*$-algebra of compact operators.
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