Let $E/K$ be an elliptic curve with complex multiplication over an imaginary quadratic field $K$. Then, I heard that it is well-known that the Tate module $V_{p}(E)$ over $\mathbb{Q}_{p}$ decomposes as direct sum of two $Gal(\overline{K}/K)$-modules.

I cannot find any literature and so let me know the elementary (and concrete) proof.