“But maybe this involves more serious physical force.”
Actually, I think the court said the exact opposite: “no proof of physical violence is required to support the domestic violence charge”
So, it appears a mere allegation is enough.
There has to be a conviction of a misdemeanor, not just an allegation. So the moral is that you should fight the misdemeanor case and not take a plea bargain.
The statute requires "physical force." The lower court said that "physical force" means "violence." All nine justices said that "violence" isn't required, but Scalia thinks that a slap isn't enough.