  In this paper, we investigate the unique continuation property for the
inequality $|\bar\partial u| \le V|u|$, where $u$ is a vector-valued function
from a domain in $\mathbb C^n$ to $\mathbb C^N$, and the potential $V\in L^2$.
We show that the strong unique continuation property holds when $n=1$, and the
weak unique continuation property holds when $n\ge 2$. In both cases, the $L^2$
integrability condition on the potential is optimal.
