Clearing props for use in movies and TV programs usually is a matter of copyright law, and sometimes trademark law too. When props include actual money, however, other laws come into play: those that prohibit counterfeiting. The question of whether it's legal to film currency has just been asked and answered, both north and south of the U.S.-Canadian border.
In the U.S., the question "Can I Film U.S. Currency?" was posted to the Cinema Law section of the blog MovieMaker and was answered by entertainment lawyer David Albert Pierce.
In Canada, the question "Do I need permission to film Canadian currency?" was answered by Bob Tarantino in Heenan Blaikie's Entertainment & Media Law Signal.
The answer in both countries: generally, it's OK to film currency for movies and TV programs, and no permission is necessary. But, as always with the law, there are nuances, explained in Pierce and Tarantino's analyses.