Duet (II) - S3.E17

Barry and team are surprised when Mon-El and Hank Henshaw arrive on their Earth carrying a comatose Supergirl who was whammied by the Music Meister. Unable to wake her up, they turn to Team Flash to save her. However, the Music Meister surprises The Flash and puts him in a similar coma, one that Team Flash can't cure. Kara and Barry wake up without their powers in an alternate reality where life is like a musical and the only way to escape is by following the script, complete with singing and dancing, to the end.

The crossover starts on Supergirl S02E16 Star-Crossed (I).