Im not saying they were looking for anyone other than sheila, but surely they would still need to confirm by way of an investigation, forensics etc that that is what happened. If not we could all get away with murder couldnt we.
police are trained to look at both sides and the whole situation, what were they going to do go back and report that jb said his sister was nuts, all the family were dead and Sc had a rifle on her body! Case closed. They still had a duty to confirm how that happened.