  Let p be an odd prime and let E be an elliptic curve defined over a quadratic
imaginary field where p splits completely. Suppose E has supersingular
reduction at primes above p. We define and study the fine double-signed
residual Selmer groups in these settings for Z_p^2-extensions. We prove that
for two residually isomorphic elliptic curves, the vanishing of the signed
{\mu}-invariants of one elliptic curve implies the vanishing of the signed
{\mu}-invariants of the other. Finally, we show that the Pontryagin dual of the
Selmer group and the double-signed Selmer groups have no non-trivial
pseudo-null submodules for these extensions.
