Dang, Indiucky! You've done well with your inhertitance with this pistol and the IJ. I am positively envious!
A valuable site regarding Colt serial numbers! Appears that it's a .25 ACP Model 1908 Vest Pocket from 1935 or 1936 from the serial number range. Should have a magazine disconnect that prevents the pistol from being fired if there's no magazine in the well (testing this with live rounds is highly discouraged). It was an additional safety feature added to the .25 ACP Vest Pocket circa 1916-1917. These are striker fired making them true hammerless. It differentiates them from the larger caliber Model 1903 .32 ACP Hammerless and Model 1908 .380 ACP Hammerless which actually have hammers concealed by the frame.
Al Capone had a number of handguns. Among them was a Model 1908 Vest Pocket .25 ACP. This model and the two, larger caliber Hammerless models were favorites among Prohibition Era gangsters as they were very easily concealed.
John