The best reference for serial number date ranges is the Standard Catalog of Smith & Wesson, currently in its 4th Edition. This book is invaluable to most of us Collectors. In addition, joining the Smith & Wesson Collectors Association gets you access to Dr. Roy Jinks, THE S&W factory historian who routinely answers ship date questions for Forum and SWCA Members.
Both the book and SWCA Membership are super great tools for those with interest in all things Smith & Wesson.
For LoveMan posting above, my Model 36 no-dash is just 61 numbers off from your serial number and mine shipped in January 1967 per Dr. Jinks. Mine has the original box, documents, and vapor paper wrapping. Yours MAY have shipped around the same time but the only way to know for sure is to ask Dr. Jinks (for free)....or send for a Letter of Authenticity ($100) thenn you'll have all the details in a written letter.
Good Luck with your Model 36....they are fine guns and iconic snubbies!
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Charlie B
SWCA#3083, SWHF#570
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