Many of the real-world data sets can be portrayed as bipartite networks. Since connections between nodes of the same type are lacking, they need to be inferred. The standard way to do this is by converting the bipartite networks to their monopartite projection. However, this simple approach renders an incomplete representation of all the information in the original network. To this end, we propose a new statistical method to identify the most critical links in the bipartite network projection. Our method takes into account the heterogeneity of node connections. Moreover, it can handle situations where links of different types are present. We compare our method against the state-of-the-art and illustrate the findings with synthetic data and empirical examples of investor and political data.