Nancy was mostly silent throughout her appearances in Sing, and mainly appeared as an accessory of sorts. She was silent towards Mike at first but never directly rejected him. She began to fall in love with him after he pulled up to the nightclub in a shiny red convertible, and phoned him sometimes, saying she missed him. She also saved his life towards the end of the film when she saw Mike on TV and that the bears were coming to get him.
They're apparently close enough that Mike trusts her with the key to his car, which enabled her to save him.
Nancy and Mike first met outside of a nightclub, not long after the events of the audition sequence. Mike discovered her walking towards the entrance and began playing the saxophone near her. She was generally impressed but didn't say anything to him. Nancy entered the nightclub and Mike was denied entry from a bouncer. Just before going in, she turned back and smiled at Mike before continuing her route. In a later scene, Mike returned to the nightclub in a red convertible car, which further earned Nancy's affection. The two then entered the nightclub with hands joined. A while later, Nancy was present with Mike as he cheated a trio of bears in a card game, but was then separated after Mike was caught and then pursued by them. She wasn't seen again until Mike's performance of "My Way", which she saw being telecast in the nightclub. The bears discovered Mike on TV and began heading to Moon Theater, which alerted Nancy to go save him. During Meena's performance of "Don't You Worry 'bout a Thing", Mike was grabbed by the three bears and taken outside. She pulled up in Mike's red convertible, moments after Mike was swallowed by the bear leader. She quickly opened the door into the bear's stomach, causing the bear to spit Mike out. He quickly got into the vehicle and Nancy drove him away from the chase. Until this point, she had not said a word in the movie. It is unknown what happened to her or Mike after these events, as they were not present during Moon Theater's grand re-opening, which was the final scene of the movie.