Riding Rules (325:60-1-19)
If a horse is ridden, drifts or swerves out of its lane in such a manner that it interferes with or impedes another horse, a foul occurs.

Stewards to Determine Interference and Placement (325:60-1-20)
The Stewards shall determine if a horse or its jockey has caused an interference and finished in front of the horse it interfered with, and, if not for the interference, the horse would have finished behind the horse it interfered with, the interfering horse shall be placed immediately behind the horse with which in interfered. If the interference is a results of dangerous riding, the stewards shall place the interfering horse in last place.