I'm not positive on yours but it's a .38 Military & Police. The serial number (581xxx dates it around 1930.
That said, you say the caliber marking is .38 S&W vs. .38 special. That, the hole for a lanyard and the CIV marking "could" mean a Victory model (SN V581xxx) with CI added later. "If" thats the case then it was made around 1943/44 time range.