how do I find out what Christmas music was use in the latest show?

Here you go:
Rockin' around the Christmas Tree (Brenda Lee)
Incidental music
Deck the Halls (jazzy instrumental)
O Holy Night (Traditional)
Jingle Bells (jazzy instrumental)
Silent Night (instrumental) This plays as Detective Chasen drinks the poison and dies. Ironic, huh?
Incidental Music
Silent Night (Traditional)
Joy to the World (instrumental)
incidental music including a little riff on the season one theme as "Santa" talks to little Trudy
O Little Town of Bethlehem (instrumental)
White Christmas (Otis Redding)
Jingle Bells (a different Jazzy instumental) over end credits

Quote:

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Jingle Bells (a different Jazzy instumental) over end credits

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That's actually the same Jazzy Instrumental version of Jingle Bells that's played earlier in the episode (starting at the end of the scene when Adrian opens his Secret Santa gift from Alice).