Absolutely. Domestic violence is no different than any other intentionally harmful act, and can be the basis for a personal injury lawsuit in Michigan civil court. As for which tort/cause of action you might bring, there are several options. You can file an intentional tort claim (such as battery and/or assault) seeking compensation for the physical injuries you have suffered.
Another option is a claim for intentional infliction of emotional distress, in order to address mental anguish and other psychological injuries. Keep in mind that these claims are not mutually exclusive and can be brought simultaneously. For additional information, click here.
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