Any liquid inc. blood which is dropped from a height will splash---blood that falls/drops from a foot onto a warm surface of the skin tends not to splash and will gel, leaving the liquid part of the blood to run. The blood would have been a pretty dark colour from her nose as it's deoxygenated blood known as venous blood which is why it wouldn't have splashed/splattered everywhere as there's no pressure from a venous bleed as there is from an arterial one where it would splatter.
I think I've got this right, as it's an important part of any investigation as to which area the blood would have come from, though this is a forensic job and not that of a police officer's.