A search finds no words to the copyrighted song title.
The copyright holder retains copyright to the music, and your adding words doesn't change that. You can perform it privately under limited circumstances (e.g., for friends without payment), but if you perform it publicly or for money then the same copyright restrictions apply to your setting as to the original piece. In fact, the restrictions may be stronger, because the "automatic license" provision may not apply after you've added words. There is a parody exception if your words comment on the song, but it's very limited.
Melodies are copyrightable. You probably can not legally use the melody without permission.
Chord progressions are not copyrightable. You may use chord progressions freely.
For a piano piece, the distinction between melody and chord progression may not be easy to determine.
As always, check with a copyright attorney. The Copyright Handbook by Nolo Press may help.