A little background:
The Regulation Police was introduced in 1917 as a square butt variant of the S&W .32 Hand Ejector, which dates back to 1896. The hand ejector name comes from the fact that this was S&Ws first gun with a cylinder that swings to the side. Prior to that S&W guns a cylinder that tipped up and had automatic ejection of the spent brass. With a solid top strap the hand ejector range was stronger that the earlier top break guns and was more suited to the higher pressures of the new fangled smokeless powder. The .32 Hand Ejector was built on the small round butt 'I' frame, which used the same grips as the earlier small caliber top breaks. In 1917 a square butt variant was introduced, the Regulation Police. At first this used a version of the round butt, which used square butt grips. After World War a square butt frame was used.
In 1950 S&W stretched the small I frame to fit the .38 Special cartridge.
This was the Chiefs Special.
In 1957 model numbers were introduced and the Regulation Police became the Model 31.
In 1961 S&W consolidated production of it's small frame revolvers on the J frame and the I frame was no longer produced.
The Model 31 became the Model 31-1, indicating the slightly larger J frame.
Your gun dates to the period between Model numbers (1957) & the change to the J frame (1961).
The change to the J frame would ultimately end the demand for the .32 Hand Ejector (Model 30) and it siblings; the round butt .38 S&W Terrier (Model 32) & the .38 S&W Regulation Police (Model 33). All were discontinued in 1974.
People after a concealable lightweight handgun would naturally choose the more powerful .38 Special Chiefs Special (Model 36) and demand for the less powerful models disappeared.
The .32 Regulation Police soldiered on until 1991 when it was finally discontinued. By that time the .32 S&W long was no longer considered an effective self defence round as it could not be loaded fast enough to cause a hollow point bullet to expand reliably.
.32 S&W ammunition is still available from manufacturers such as Winchester and it is a fine target round.
As roughly a million of the .32 Hand Ejector and Regulation Police were manufactured, value is not high. In 2006 the Standard Catalog of S&W gave a value of $275 in excellent condition.