Unless inspection gives you good reason to believe the barrel has been changed, it may not have been. The Model 64-1 was initially ordered by the OHP as a .357 Magnum version (4" barrel), but all of the .357 Magnum units did not go to that agency. However, that configuration soon became the Model 65, so by 1976 (your serial number) it is a bit surprising that one exists, regardless of barrel length. But with S&W just about anything is possible. Yours might be worth a letter.

It should be noted that the Model 64-1 chambered for the .38 Special continued in production until 1977. During the 1972-76 period, the Models 64 and 64-1 were made concurrently. The former had a tapered barrel, while the latter had the heavy barrel. They were replaced by the -2 and -3.

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Jack
SWCA #2475, SWHF #318