Yes, if you got the book (catalog), you could tell approximately which year it was manufactured.
If you don't have the book, or don't know who has the book, my suggestion is that you log into S&W Forum (smith-wessonforum.com) and ask the people there. Many of them are experts of S&W revolvers and have the book.
If your gun looks like a collectable piece, and you want more information such as when it was manufactured, when it was shipped, and where (to whom) it was shipped to, at what price, you have to send a cheque of US$35 to the historian in S&W, whose name is Roy Jinks. He will look for all historical records in the company, and send a Letter of Authentication to you.
But this usually takes 2 - 4 months.
However, it is worth the wait if your gun is old but in good condition. The letter adds value to the resale price.