This is governed by the provisions of 18 U.S.C. 504 Printing and filming of United States and foreign obligations and securities. As for filming money, look to paragraph 3 of that section.
(3)The making or importation of motion-picture films, microfilms, or slides, for projection upon a screen or for use in telecasting, of postage and revenue stamps and other obligations and securities of the United States, and postage and revenue stamps, notes, bonds, and other obligations or securities of any foreign government, bank, or corporation. No prints or other reproductions shall be made from such films or slides, except for the purposes of paragraph (1), without the permission of the Secretary of the Treasury.
Based on this statute, it appears that filming of money is not expressly forbidden. Before doing any filming, consult your attorney about the specifics of your project. He or she will map the project on this statute and can provide you advice regarding the impact of any potential copyright infringement liability. You can read more about copyright issues at http://www.usmint.gov/policy/index.cfm?action=TermsOfUse#rights
Answered on Dec 30th, 2010 at 4:43 PM