Steve Martin and Carmen Cusack on Broadway musical "Bright Star"

Comedian Steve Martin is also an accomplished actor, producer, writer and musician. And he just added another job to his impressive resume.

The Grammy and Emmy Award winner has taken his musical talents to Broadway, writing and composing the new musical, "Bright Star," with singer-songwriter Edie Brickell. The musical is nominated for five Tony Awards.

It tells a "hypothetical story" based on a true event. Brickell came across a 1904 newspaper article about an abandoned baby that survived after being thrown from a train in a suitcase.

"Our musical tells the story of what possibly could've happened, in a very joyous way," Martin told "CBS This Morning" Tuesday.

Carmen Cusack stars as Alice Murphy, a precocious teenager who grows up to be the editor of a literary journal. Cusack said she felt like she knew the character "immediately," especially given a personal connection to her role.

"My mother had me when she was 16 and that was an issue that had to be dealt with," Cusack told "CBS This Morning." "She grew up in a very religious background and there was a lot of discussion of what they should do with this unborn child. But here I am and thank goodness."

Martin described Cusack, who's making her Broadway debut, as a "true discovery." Cusack first auditioned for the gig, recording herself on a CD in her California apartment. She stuck through a long audition process, and has been with the show since the first reading.

"We thought, 'she's good, let's hire her.' But you don't know someone's going to last and sustain for the next four years, through every iteration of the musical," Martin said.

Cusack also complimented Martin for his "sensitivity."

"He seemed very open and very warm and incredibly sensitive," Cusack said. "He would watch every little movement in your face and if you felt like a line wasn't working, he would pretty much immediately catch on -- just by a little quirk in my face or something, he would know."

Martin is known for his big screen hits like "Father of the Bride" and classic comedy skits on "Saturday Night Live," but he has also established a name for himself as a musician. He's played the banjo since he was a teenager. And last year, he was honored by the International Bluegrass Music Association with a distinguished achievement award, for introducing film and television fans to the genre through his musical collaborations with Edie Brickell and the Steep Canyon Rangers.

His song with Brickell, "Love Has Come For You," won a Grammy for Best American Roots Song in 2014. He partnered with Brickell -- whom he described as a "musical genius" -- to compose the music for "Bright Star."

"This really came about because... [of] a discussion with Edie that we really liked the music that we were raised on and how much they really affected our lives in a positive way. And felt our songs that we write together are melodic... and we just started doing it," Martin said.

He also sought to correct the "bad" impression some people have of the banjo.

"They think it's one thing, but the banjo, it can be quite melancholy, as you could hear in the songs. And it evokes something to Americans, I feel -- something they sense that's a part of them, when they really play it in the way that I like to hear it," Martin said. "It's very evocative."

Lucky audience members can also be treated to a performance by Martin, as he plays the banjo during the musical's intermissions some five times a week.

"It's the biggest reward for the least work I've ever done," Martin said.

Like the music, the play itself is filled with emotions and drama, but -- as you might already assume from Martin's history as a comedian -- also humorous moments.

"By the end of it, I kind of feel revived because it's like after having a big cry and then all of a sudden, you start laughing at the end," Cusack said. "That's how I feel at the end of it and I hope that's how the audience goes out leaving."