Sense-making software for crime investigation should be based on a model of reasoning about evidence that is both natural and rationally well-founded. A formal model is proposed that combines AI formalisms for abductive inference to the best explanation and for defeasible argumentation. Stories about what might have happened in a case are represented as causal networks and possible hypotheses can be inferred by abductive reasoning. Links between stories and the available evidence are expressed with evidential generalisations that express how observations can be inferred from evidential sources with defeasible argumentation. It is argued that this approach unifies two well-known accounts of reasoning about evidence, namely, anchored narratives theory and new evidence theory. After the reasoning model is defined, a design is presented for sense-making software that allows crime investigators to visualise their thinking about a case in terms of the reasoning model.