Yes. There are many laws against domestic violence. The most recent is PWDVA, passed in 2005, which is a civil law that prevents economic, verbal, sexual, emotional, and physical domestic abuse.
Most of the time, domestic violence cases do not end up in a trial. A defendant will plead guilty or no contest and enter a plea agreement. Only if the defendant pleads not guilty will there be a trial, at which point the victim will usually need to testify.
There are plenty of cases where police officers arrive at the scene and make incorrect assessments as to what events have transpired. When an individual is falsely charged with domestic violence, they can work with a domestic violence attorney to develop a sound legal defense.