During the investigation, police say they found a video in the man's home that showed him sexually molesting cows in 2006.
Judge James Morley ruled Wednesday that prosecutors did not present enough evidence to jurors that Melia's alleged actions tormented the animals on a Southampton farm.
The judge made clear that he doesn't think the alleged action is OK.
Melia and former girlfriend Heather Lewis remain charged with molesting the three girls.
Information from: Burlington County Times