While not probable,it is possible because serial numbers were not mandated until the year 1968 with the passage of the gun control act by congress that year.
Your serial number indicates that your Smith and Wesson 38 special was made in the Year 1960.
No serial number = no answer.
Email smith and Wesson for the answer
Call S&W
No serial number given.
Impossible to answer without the serial number.
If you contact Smith & Wesson, they will give you that information.
Smith&Wesson model 14
By the serial number.
$9.92
1955 -1956
1963-65.