Step 1: Recall cleistogamous flowers.
Cleistogamous flowers never open. Hence, pollination occurs within the same flower.
Therefore,
\[
\boxed{\text{Cleistogamous flowers always show autogamy}.}
\]
Step 2: Examine the remaining statements.
Chasmogamous flowers may undergo autogamy, geitonogamy or xenogamy depending on the pollinating agent.
Hence, statements (B), (C) and (D) are incorrect.
Step 3: Choose the correct option.
Thus, the correct option is
\[
\boxed{(A).}
\]