As Koutarou has not inspected it closely, he didn't know it didn't have a serial number. Not that he knows much about serial numbers on guns, like where to look or how they're given, or anything of the sort.

He knows though that Togusa knows far more about these sort of things than he ever will know, and he nods slowly. "You're the one who knows how the weapon laws might work... If that's what it would have to be registered as then I will do so, though I don't really know what papers one fill out..... Nor did I ever think I would need to know."