The letter "C" at the beginning of the serial number is nothing more than a prefix for a range of gun made during a certain period of time. There are likely thousands, if not tens or even hundreds of thousands, of S&W Model 10's with a "C" prefix serial number. If you want more specific information about the gun, you will need to provide the whole serial number (you can leave out the last two or three digits if you prefer as many people don't like to post the entire serial number on the internet) and then someone with a copy of
The Standard Catalog of Smith & Wesson can give you the year of manufacture.
If you want more specific information still, you'll need to get a factory letter for S&W historian Roy Jinks. If you want a factory letter, your best bet would be to send Mr. Jinks a detailed description of your revolver including the model, caliber, barrel length, finish, grip frame type (round butt or square butt), and any other pertinent information along with the full serial number (don't leave any part out), and, if possible, photos of the gun from multiple angles. The current cost of a S&W factory letter is $50 and can provide information as to the specific gun's original configuration as it left the factory (this will let you know if the gun as been modified over the years) as well as the date it was originally shipped and to whom (or what distributor/retailer/police department/military unit) is was shipped from the factory to.
http://www.smith-wesson.com/webapp/wcs/stores/servlet/Category4_750001_750051_757825_-1_757814_757812_image
http://www.smith-wesson.com/wcsstore/SmWesson2/upload/other/LOA.pdf
If your revolver was actually used in the film you mentioned and the production company or prop house bought it directly from S&W, then a factory letter might give you the information you seek. If, however, your gun was shipped to a regular gun distributor and then purchased by the production company/prop house later then a factory letter probably wouldn't tell you much. If you suspect that the latter case is more likely, your best bet would probably be to attempt to contact the production company and/or prop house used when the film was made.
