In 2010, the conservative group Wisconsin Family Action filed a lawsuit claiming the registry violates the 2006 state constitutional amendment banning same-sex marriage.
The registry grants same-sex couples some legal rights, including control over property inheritance and allowing for hospital visitations.
The plaintiffs allege a portion of the amendment prohibits substantially similar institutions to marriage and the qualifications to get married and get on the registry are very similar.
The defendants are Fair Wisconsin, the state's largest gay rights group. It believes the law is constitutional because it grants only a fraction of the rights currently afforded to married couples.
The registry was upheld by a state appeals court last year.
A final ruling from the Wisconsin Supreme Court could take months.