Leyva, who has co-written the book "My Sister" with her sibling Marizol to document their experience, relied on the activist for support while on set.
"Laverne and I had our conversations, I told her I had a transgender sister," Leyva tells People magazine. "But I was so thrilled, not only that the character had so many layers and was beautifully written, but also Laverne's ability to convey her thoughts and feelings in a way that made you listen, that I knew would be really impactful."
The 47-year-old's connection to Cox was made all the more special during a pivotal moment when Marizol first spoke openly of being a trans woman.
"Then about a year after we met, I got to present Laverne with an award and Marizol attended the ceremony with me," she adds. "It was the first time that I declared to the world, to everyone in that room, that I had a transgender sister.
"It was also the first time Marizol had vocally said, 'Yes, I am a trans woman.' It was through the platform that Laverne and that Orange Is the New Black had created for us."
Leyva's book, "My Sister: How One Sibling's Transition Changed Us Both", is available on March 24.