Filming currency can arise in a variety of circumstances: from filming actors exchanging money to using images of money in the opening titles of a film (e.g., a fan of bills of various denominations or a shower of coins in an opening montage to illustrate gambling or some kind of monetary success) to filming close-ups for purposes of illustrating a point in a documentary. Is anybody's permission required to film Canadian currency?
The basic answer is that if you are filming Canadian paper currency for use in a film or TV project you generally do not need permission. The Bank of Canada helpfully publishes a Policy on the Reproduction of Bank Note Images, which states the following:
It is not necessary to request the Bank's permission to use bank note images for film or video purposes, provided that the images are intended to show a general indication of currency, and that there is no danger that the images could be misused.
The corollary of that exception is that in other circumstances (i.e., if the images are intended to show something other than a general indication of currency or where there is a danger that the images could be misused), then permission is required - and that permission can be obtained from the Bank of Canada, which owns copyright in Canadian currency. (An online request form is available from the BoC here.) The Bank's policy states that "The Bank will usually consent if there is no counterfeiting risk and if the intended use is in good taste." It is possible to imagine uses which may run afoul of the policy (e.g., a close-up image of a bank note which is then defaced with crude imagery or writing, or an animated treatment which starts with a real bank note but then is modified to incorporate offensive imagery), but those will presumably arise infrequently.
One matter not expressly covered by the Bank's policy is whether permission is required to film Canadian coin currency - the Bank's policy covers only paper notes. And the reason for that is because the Bank of Canada does not own the intellectual property rights in Canadian coin currency - the Royal Canadian Mint does. The Mint has its own policies regarding the use of the Mint's intellectual property (which includes "coin images", "drawings" and "creative designs"), including an application form. The Mint's policies, unlike those of the Bank, do not start with the premise that no permission is required for purposes of filming, and so technically permission should be sought in order to avoid a potential infringement claim.
[Inspiration for this post was provided by David Albert Pierce, Esq., writing at the MovieMaker blog: Cinema Law: Can I Film U.S. Currency?, which provides a detailed explanation of US law on the matter. Dan Ciraco's "The Money Shot: The Law Surrounding the Reproduction of Bank Note Images" (Ontario Bar Association Entertainment Media and Communications Section Newsletter 15(1) (Nov 2005)) is an invaluable resource of Canadian law on the topic.]