It is. Michigan would need to change it's Constitution or have a court rule against it
Michigan Marriage/Relationship Recognition Law
Licenses marriages for same-sex couples? No.
Honors marriages of same-sex couples from other jurisdictions? No.
Michigan law states: “Marriage is inherently a unique relationship between a man and a woman. As a matter of public policy, this state has a special interest in encouraging, supporting, and protecting that unique relationship in order to promote, among other goals, the stability and welfare of society and its children. A marriage contracted between individuals of the same sex is invalid in this state. … Except as otherwise provided in this act, a marriage contracted between a man and a woman who are residents of this state and who were, at the time of the marriage, legally competent to contract marriage according to the laws of this state, which marriage is solemnized in another state within the United States by a clergyman, magistrate, or other person legally authorized to solemnize marriages within that state, is a valid and binding marriage under the laws of this state to the same effect and extent as if solemnized within this state and according to its laws. This section does not apply to a marriage contracted between individuals of the same sex, which marriage is invalid in this state unclear.”
The Michigan Constitution states: "To secure and preserve the benefits of marriage for our society and for future generations of children, the union of one man and one woman in marriage shall be the only agreement recognized as a marriage or similar union for any purpose."
Source
http://www.hrc.org/laws-and-legislation/entry/michigan-marriage-relationship-recognition-law
= new reply since forum marked as read