Recently, there is growing concern that machine-learning models, which currently assist or even automate decision making, reproduce, and in the worst case reinforce, bias of the training data. The development of tools and techniques for certifying fairness of these models or describing their biased behavior is, therefore, critical. In this paper, we propose a \emph{perfectly parallel} static analysis for certifying \emph{causal fairness} of feed-forward neural networks used for classification of tabular data. When certification succeeds, our approach provides definite guarantees, otherwise, it describes and quantifies the biased behavior. We design the analysis to be \emph{sound}, in practice also \emph{exact}, and configurable in terms of scalability and precision, thereby enabling \emph{pay-as-you-go certification}. We implement our approach in an open-source tool and demonstrate its effectiveness on models trained with popular datasets.