The father says the woman who gave birth to the twins is actually just a surrogate and has no genetic link to the babies. However, the woman says she gave birth to the infants and she never agreed to be just a surrogate, that she wanted to co-parent the twins with McMurray.
Cindy Close never expected to be in court, battling for parental rights to the twin boy and girl she gave birth to earlier this year.
"They're trying to say I'm never the mother of my children, and I am their mother. No matter how it turns out, I am their mother. I gave birth to them, I loved them when they were inside my body. I planned to raise them," Close said.
But Monday afternoon, Close and her lawyers faced off against the children's biological father, Marvin McMurray. McMurray's attorneys say since the children were fathered by him with donated eggs, Close has no genetic link to the children, and is not their mother.
"My children are involved, and they're minors and we're in litigation," McMurray told Eyewitness News.
"But you don't think Ms. Close should have any relations with your children?" we asked him.
Attorney Sarah Arvidsson stepped in and said, "We're not going to give any comments at this time, just due to the very sensitive nature of these proceedings and that we're in the middle of litigation, thank you."
The case is drawing national attention because the basic argument hinges on what the definition of a mother is. Close says even though she and McMurray had no romantic involvement, they had agreed to co-parent the twins. But McMurray's attorney disagrees, though she won't discuss her arguments to us.
"These are children, live human beings, and nothing says that their best interest would be served by being in the media," McMurray's attorney, Ellen Yarrell said.
Both sides are arguing their case in Judge Bonnie Hellum's court. But to Cindy Close, the argument is a simple one.
"If they decide I'm not the mom here, it could affect could moms everywhere who want to use donor eggs," she said.
After a four-hour court hearing, Cindy's claim of motherhood remained in limbo, with only the promise of another day in court.
"We'll know next month. She doesn't know her status with the kids she gave birth to," Close's attorney, Grady Reiff, said.
For now, Close visits the twins daily at the home of McMurray's partner.