Surfaces with self intersection in 3-space

Question

Let $F$ be a sphere in the Euclidean 3-space $\mathbb{R}^3$ With self intersection. Let $C$ be a double point circle in $F$. Then the double circle $C$ must bound a 2-disk in the standard sphere (sphere without self intersection). Suppose the surface is with non-zero genus, then in this case how can we describe $C$, of course it is no longer on the boundary of a 2-disk.