It's not obvious. Blood can and does leave a body after someone is already deceased and as someone is dying there's changes in their pathology.
And there's several ways to test it. For one, the pH in blood immediately changes upon death. Blood also changes colour after death. Coagulation is different in blood after death.
Decomposition starts instantly upon death. Maybe you're confusing decomposition with putrefaction. Putrefaction takes days, but that's the last stage of the decomposition process.
Death is likely to result in very extensive biochemical changes in all body tissues due to lack of circulating oxygen, altered enzymatic reactions, cellular degradation, and cessation of anabolic production of metabolites. These biochemical changes may ...
www.ncbi.nlm.nih.gov
Most people expel urine and saliva and defecate immediately upon death. They wouldn't just be looking for blood. They'd be looking for any tissue with Williams DNA, IMO