Laura Palmer has disappeared, the Twin Peaks name has been usurped by a depressing chain of breastaurants, making Internet research on this subject annoying and potentially troublesome (based on the keylogging trail we're leaving behind at work).
Fair use? Your proposed use seems like a fair use (for which permission is not required). The amount taken is small and it is being used a for a purpose not intended by the copyright owners (a transformative use).
Just in case dept. If you're not comfortable claiming fair use and you'd rather get permission, we think the owner of rights is Twin Peaks Productions, Inc. (formerly Lynch/Frost Productions). According to California corporations records, the company can be contacted either care of Hansen, Jacobson, Teller and Hoberman, 450 N. Roxbury Drive, 8th Flr., Beverly Hills, CA, 90210, or via Fred Altman, 9255 Sunset Blvd. #901, Los Angeles, CA, 90069. You can also review the history of copyright transfers for Twin Peaks by searching Copyright Office records -- search for "Twin Peaks" here.
BTW Dept. Twin Peaks Productions, Inc. chased an infringer in a 1993 fair use case.