Can you explain how you saw smoke in the crankcase? Was this in the oil filler tube? Also what color is the smoke ?
Not sure which type you have, but I believe your engine service manual should be available here:
Service & Owners Manuals - Service & Support - Kohler Engines
This is the section that I thought relavent to your problem:
A spring steel reed and stop is mounted on each bank of the crankcase, between the lifter bores. When the pistons move downward, air is pushed past the reeds into the cylinder head cavities. On the #2 cylinder, the upper end of the head is completely sealed by the rocker cover, so a low, positive pressure is created in the head cavity. The #1 rocker cover has a hole in it for venting. The bottom nipple of an oil separator canister is fitted into the hole with a grommet. From the top nipple of the canister, a breather hose goes back to the air cleaner base. The air moving into the #1 head cavity is filtered
Through the oil separator and then is drawn into the air intake. The upward travel of the pistons closes the reeds and creates a low vacuum in the lower crankcase. The combination of low pressure above and low vacuum below forces any accumulated oil out of the #2 head area into the crankcase. On the #1 bank you have atmospheric pressure above and vacuum below, again drawing any oil toward the crankcase.
I assumed a blockage in this section, however if you see smoke in the case itself, then I don't see how this could be the reason