No other Reds were among the leaders at their positions.
Batting .298/.324/.497 with six home runs and 18 RBIs through Tuesday, Cozart leads Cincinnati in hits and batting average this season. Among qualified NL shortstops, he is ranked third in hitting.
In 2015, Cozart was lost for the season when he slipped and fell running over first base on June 10. He needed reconstructive right knee surgery.
Fans can cast their votes for starters at MLB.com and all 30 club sites -- on their computers, tablets and smartphones -- exclusively online using the 2016 Esurance MLB All-Star Game Ballot until Thursday, June 30, at 11:59 p.