Across 2,228 ranked games on patch 16.21 in Master and above, Katarina mains win 53.5% of their games in the mid lane.
Their most common build appears in 46.8% of those games and wins 55.2% of its 1,042 games.
It starts 
Dark Seal and 
Refillable Potion, completes 
Lich Bane, 
Shadowflame, 
Zhonya's Hourglass, 
Rabadon's Deathcap and 
Void Staff in that order, and takes 
Sorcerer's Shoes.
Three other builds are played often enough in the mid lane to be measured on their own.
In the mid lane, Katarina mains fare best against 
Taliyah (won 81.3% of 16 games), 
Twisted Fate (won 68.4% of 57 games) and 
Ryze (won 71.0% of 31 games).
Their hardest matchups, the champions that counter Katarina, are 
Annie (won 31.6% of 19 games), 
LeBlanc (won 41.2% of 51 games) and 
Vex (won 36.0% of 25 games).