I've seen many people on Purim who wear their clothing inside out, in the spirit of ונהפוך הוא. Yet the Mechaber writes explicitly (SA OC 2:3):
ידקדק בחלוקו ללובשו כדרכו שלא יהפוך הפנימי לחוץ
He should be particular with his cloak to wear it properly, that the inside not be turned outside.
Now, crossdressing may be permissible on Purim, depending on your posek and rationale. I'd imagine turning one's garment inside-out, which is simply a matter of looking respectable (Mishnah Berurah ad. loc.), is a much lesser prohibition and so should be permitted. Nevertheless, are there any sources which explicitly address this one way or another?