In this paper, certain connections between complex symmetric operators and anti-automorphisms of singly generated
C
∗
C^*
-algebras are established. This provides a
C
∗
C^*
-algebra approach to the norm closure problem for complex symmetric operators. For
T
∈
B
(
H
)
T\in \mathcal {B(H)}
satisfying
C
∗
(
T
)
∩
K
(
H
)
=
{
0
}
C^*(T)\cap \mathcal {K(H)}=\{0\}
, we give several characterizations for
T
T
to be a norm limit of complex symmetric operators. As applications, we give concrete characterizations for weighted shifts with nonzero weights to be norm limits of complex symmetric operators. In particular, we prove a conjecture of Garcia and Poore. On the other hand, it is proved that an essentially normal operator is a norm limit of complex symmetric operators if and only if it is complex symmetric. We obtain a canonical decomposition for essentially normal operators which are complex symmetric.