Finesse is an attribute in Omerta City of Gangsters
Finesse determines a character's proficiency with all firearms. It seems proficiency has nothing to do with damage according to testing and is possibly only related to accuracy.
Finesse is accuracy with a gun. I believe each point in finesse will add 5% to hit to the shot. For example on someone with 9 finesse at a certain distance will have 80% chance to hit the target if in the same exact spot and gun another guy with 7 finesse will have a 70% chance to hit. Also it's important to note that 80% is the highest accuracy you can achieve without using the Aim that costs 1 AP which gives 15% more accuracy to any attack. Lastly you must remember all this testing was done with the pistol and could possibly change with different weapons.
Marksmanship = Finesse * 2