  In this paper, we consider a vector-valued one-phase Bernoulli-type free
boundary problem on a metric measure space $(X,d,\mu)$ with Riemannian
curvature-dimension condition $RCD(K,N)$. We first prove the existence and the
local Lipschitz regularity of the solutions, provided that the space $X$ is non
collapsed, i.e. $\mu$ is the $N$-dimensional Hausdorff measure of $X$. And then
we show that the free boundary of the solutions is an $(N-1)$-dimensional
topological manifold away from a relatively closed subset of Hausdorff
dimension $\leqslant N-3$.
