Abstract The size of a partly observed population is often estimated with the capture-recapture model. An important assumption of this chat model is that sources can be perfectly linked. This assumption is of relevance if the identification of records is not obtained by some perfect identifier (such as an id code) but by indirect identifiers (such as name and address). In that case, the perfect linkage assumption is often violated, which in general leads to biased population size estimates. Initial suggestions to solve this use record linkage probabilities to correct the capture-recapture model. In this article we provide a general framework, based on the standard log-linear modelling approach, that generalises this work towards the inclusion of additional sources and covariates. We show that the method performs well in a simulation study.