This adaptation of an Ellery Queen mystery concerns the theft of a rare Chinese stamp (the Mandarin of the title), which takes place in a hotel with several shifty characters and an hysterical manager (the priceless Franklin Pangborn). The mystery, such as it is, concerns both the stamp theft and two murders, and shows Ellery and his father the Inspector as a team rubbing together just enough to solve the case.
You can stream The Mandarin Mystery (1936) free and legally on OldReel, via the Internet Archive.
Yes — it is in the public domain and can be watched and shared freely.