In Ohio the owner of the Cow could be responsible. Here is a description of a court case:
http://www.law.utexas.edu/dawson/cases/car/sellars.htmThe article says:
R.C. 951.02 provides:
No person, who is the owner or keeper of horses, mules, cattle, sheep, goats, swine, or geese, shall permit them to run at large in the public road, highway, street, lane, or alley, or upon unenclosed land, or cause such animals to be herded, kept, or detained for the purpose of grazing on premises other than those owned or lawfully occupied by the owner or keeper of such animals.