To what extent can a character quote, sing the lyrics, or hum the tune of a song without rights or permission being attained?
Ultimately, that issue would have to be addressed by whoever’s handling the legal affairs for the movie. Believe me, it will come up when it needs to.
For your purposes in writing a screenplay, don’t worry about it. Don’t footnote, don’t asterisk, don’t put a special note in the script. You can leave it as simple as:
- Max is WHISTLING the "Bewitched" theme when a pitbull suddenly attacks his car.
If it’s especially important to show the lyrics of a song, put them in a character’s dialogue block. Remember that sung words are generally italicized.