Sounds like a .32 Long Rimfire case to me. The dimensions are near enough.
Or, the empty case might not be a firearm case at all. Some nail drivers use a .32-caliber rimfire blank. I have one in my cartridge collection and its dimensions are close enough. Mine has a U headstamp, attesting to its manufacture by Remington under the UMC brand.
Back to the .32 Long Rimfire:
This cartridge was introduced in the Smith & Wesson New Model No. 2 revolver in 1861. The cartridge was quickly picked up by other pistol-makers and chambered in handguns to probably the early 1900s.
It was also popular in rifles, beginning in the 1880s or 1890s. The last .32 Long Rimfire rifle was made by Stevens, in the 1930s. I have a Marlin Model 1892 lever-action rifle that, with a firing pin change from center to rimfire, is made for the .32 Long Rimfire.
.32 Long Rimfire ammunition is still imported, on occasion, from Brazil. I believe that Old Western Scrounger still sells it.
Sounds like someone had an old revolver or rifle they wanted to try.
I am uncertain about the A headstamp.
If it is an A with raised lettering, and a copper case, it is a very old cartridge and perhaps made by the American Metallic Cartridge Company of Coventry, Conn. This company existed from about 1870 to the 1880s.
If so, someone just popped off a nice collector's cartridge. Probably didn't have any idea of this old cartridge's value.
If the case is copper, it's likely made before about 1948. If brass, some time after.
The last American-made copper cases were .22 rimfires made by Remington, I believe, in 1948. As far as I know, all rimfire ammo today is made with brass cases.
