Is the victim required to report the abuse? That's what I'm trying to deal with here, what should the victim's response be from a biblical perspective.
Perhaps the clearest passage can be found here.
Romans 13:1-7
1 Every person is to be in subjection to the governing authorities. For there is no authority except from God, and those which exist are established by God.
2 Therefore whoever resists authority has opposed the ordinance of God; and they who have opposed will receive condemnation upon themselves.
3 For rulers are not a cause of fear for good behavior, but for evil. Do you want to have no fear of authority? Do what is good and you will have praise from the same;
4 for it is a minister of God to you for good. But if you do what is evil, be afraid; for it does not bear the sword for nothing; for it is a minister of God, an avenger who brings wrath on the one who practices evil.
5 Therefore it is necessary to be in subjection, not only because of wrath, but also for conscience’ sake.
6 For because of this you also pay taxes, for rulers are servants of God, devoting themselves to this very thing.
7 Render to all what is due them: tax to whom tax is due; custom to whom custom; fear to whom fear; honor to whom honor.
Every person is under subjection both abuser and the abused. Abuse is a crime and we are under obligation to report crime to the authorities. Some positions ie: pastor, school teachers, healthcare, etc. carry a heavier responsibility. If the abused will not or cannot report the crime then someone with direct knowledge of the crime is obligated to report it. Justice is a minister of God for good and evil. It is dealt in different ways as the text indicates.
If you are dealing with a case of spouse abuse you will hear, "but I love him." more often than "arrest that man." Consider the vows taken at marriage, typically to love, honor and cherish for better/worse, richer/poorer in sickness/health. How is love demonstrated with a fist or weapon? How can someone be honored and abused at the same time? You cannot cherish and choke at the same time. The abuser has already demonstrated the vows spoken before God and witnessed by man meant nothing. There would be a stronger argument that the abuser has sent her away (even if not physically) than to believe she retains an obligation to stay.
Your profile says you teach HS math. What are you required to do at school? If you fear a conflict between your obligations to the school district and to your Lord, rest easy Brother. There isn't one.
If you are dealing with an actual situation and not theory, email me with all haste.