Perhaps not in general (I don't know either way), but in the specific case of domestic violence, there is absolutely a societal bias (US perspective, here) against men who accuse a woman of domestic violence. In many places it's even considered "funny" that a man was "hurt by a girl", to the point that a man would never even consider reporting something like this.

Unfortunately, it's of course not all roses on the other side: while people certainly believe in the abstract that women experience domestic violence, there's still often a lot of bias against specific women when they accuse a male partner of domestic violence. ("But he seems like such a nice guy, I could never believe he'd do something like that!", etc.)