A C*-algebra $A$ is C*-reflexive if any countably generated Hilbert C*-module
$M$ over $A$ is C*-reflexive, i.e. the second dual module $M''$ coincides with
$M$. We show that a commutative C*-algebra $A$ is C*-reflexive if and only if
for any sequence $I_k$ of disjoint non-zero C*-subalgebras, the canonical
inclusion $\oplus_k I_k\subset A$ doesn't extend to an inclusion of $\prod_k
I_k$.