  Let $p\ge5$ be a prime number. Let $E/\mathbb{Q}$ be an elliptic curve with
complex multiplication by an imaginary quadratic field $K$ such that $p$ is
inert in $K$ and that $E$ has good reduction at $p$. Let $K_\infty$ be the
anticyclotomic $\mathbb{Z}_p$-extension of $K$. Agboola--Howard defined
Kobayashi-type signed Selmer groups of $E$ over $K_\infty$ and showed that
exactly one of them is cotorsion over the corresponding Iwasawa algebra. In
this short note, we discuss a link between the characteristic ideals of the
cotorsion signed Selmer group and the fine Selmer group building on a recent
breakthrough of Burungale--Kobayashi--Ota on the structure of local points.
