I think the closest you can get with a general inquiry is "probably 1940." You can order a history letter from S&W for $50 that will give you the exact shipment date and the identity of the recipient -- usually a hardware store or regional distributor, but sometimes an individual or a law enforcement agency.
A problem with dating is that S&W recorded shipping dates, not manufacture dates, and did not even follow a policy of shipping in serial number order. So we know that many guns in the 60xxx serial number range shipped in 1940, but any one gun could have shipped in almost any month from January to December.
That sounds like a great revolver. Can you show us pictures? We love pictures.