I just asked my advisor about this, a retired chair and someone who has been around the residency application game for a while. He said one single letter to the chairman/program director is sufficient, but you may want to mention all the administration--something along the lines of "Dear Dr. PD, I would like to thank you, Dr. So-and-so (Chair) and Dr. XYZ (Assistant PD) for the opportunity to interview...blah blah blah." Somewhere else you may want to mention "how insightful meeting with Dr. A, Dr. B and Dr. C (the interviewers)". He also said to type it, not hand write it--this is still a business interview, not a date.
I am only writing an additional letter if I really hit it off with someone, and in that case I am sending an email. I sent a hand written thank you card only to an attending (and his wife) who hosted the pre-interview dinner in their home, and that was a "thank you for your hospitality" type card, and kept is rather formal.
Just my experience, though!