Would have to at least know the frame size.
Your serial number indicates that your Smith and Wesson 38 special was made in the Year 1960.
Email smith and Wesson for the answer
No serial number = no answer.
If you contact Smith & Wesson, they will give you that information.
Smith&Wesson model 14
Impossible to answer without the serial number.
No serial number given.
Call S&W
1955 -1956
1963-65.
By the serial number.
Made @ 1964.