In a trial that begins Monday, eight gay and lesbian couples argue the state's refusal to grant marriage licenses violates their constitutional rights and denies them the financial, social and emotional benefits of marriage.
A ruling in their favor could have nationwide implications for states that have adopted or are considering civil union-like legislation. Connecticut in 2005 passed a civil unions law, which state officials say gives same-sex couples the equality they seek.
Massachusetts is the only state in the U.S. to allow same-sex couples to marry. Connecticut and five other states - Vermont, California, New Jersey, Maine and Washington - have laws allowing either civil unions or domestic partnerships. Hawaii extends certain spousal rights to same-sex couples and cohabiting heterosexual pairs.
Anne Stanback, president of the group Love Makes a Family, said outside the court Monday that she and her partner of 23 years have not had a civil union, but have been waiting for full marriage rights.
"What is unique here in Connecticut is that we're going into this having civil unions on the book," she said. "So the more unique challenge will be showing what is the harm when you have the state rights of civil unions but not the full equality of marriage."
The Connecticut couples say civil unions are inferior to marriage and violate their rights to equal protection and due process.
Married couples have federal rights related to taxes, Social Security beneficiary rules, veterans' benefits and other laws that people in civil unions don't have.
Because civil unions aren't recognized nationwide, other rights, such as the ability to make medical decisions for an incapacitated partner, disappear when couples cross state lines.
The Connecticut couples' claim was dismissed by a lower court last year when a judge said they received the equality they sought when Connecticut passed a same-sex civil unions law. The couples appealed.
The state's attorney general, Richard Blumenthal, argues that the rights and benefits are identical, whether the union is called a civil union or a marriage.
A bill is pending in Connecticut's state legislature to approve same-sex marriage, but leaders of the Judiciary Committee say they want to pull it from consideration this session because they do not believe enough lawmakers would vote to approve it.
Republican Governor M. Jodi Rell, who signed the civil unions bill into law in 2005, has said she would veto a gay marriage bill. Rell has said she believes marriage is between one man and one woman.
Connecticut's Supreme Court will not rule immediately Monday after the arguments are presented. It is not expected to announce its decision until later this year.
A similar case is pending before California's high court.