The song was written by Mack Gordon, lyrics, and Harry Warren, music. The song is lip-synched by Lynn Bari in the movie Sun Valley Serenade. Pat Friday sang the vocals with John Payne and The Modernaires. The single, RCA Bluebird B-11230-A, reached no. 18 on the Billboard pop singles chart in a one-week chart run. The single release featured vocals by Paula Kelly and The Four Modernaires. The B side of the single was "Chattanooga Choo Choo", which de facto, was treated as the A side.

Based on this passage, who wrote i know why and so do you? Let's give stream of consciousness first:
To answer this question, we should know that: The song was written by Mack Gordon, lyrics, and Harry Warren, music.
So, the final answer is Mack Gordon , lyrics , and Harry Warren , music.