Summary: A 2-partition of a graph \(G\) is a function \(f:V(G)\rightarrow \{0,1\}\). A 2-partition \(f\) of a graph \(G\) is a locally-balanced with an open neighborhood, if for every \(v\in V(G)\), \(\left\vert \vert \{u\in N_G(v)\colon\,f(u)=0\}\vert-\vert\{u\in N_G(v)\colon\,f(u)=1\}\vert \right\vert\leq 1\). A bipartite graph is \((a,b)\)-biregular, if all vertices in one part have degree a and all vertices in the other part have degree \(b\). In this paper we prove that the problem of deciding, if a given graph has a locally-balanced 2-partition with an open neighborhood is NP-complete even for \((3, 8)\)-biregular bipartite graphs. We also prove that a \((2,2k+1)\)-biregular bipartite graph has a locally-balanced 2-partition with an open neighbourhood if and only if it has no cycle of length \(2 \pmod 4\). Next, we prove that if \(G\) is a subcubic bipartite graph that has no cycle of length \(2 \pmod 4\), then \(G\) has a locally-balanced 2-partition with an open neighbourhood. Finally, we show that all doubly convex bipartite graphs have a locally-balanced 2-partition with an open neighbourhood.