The home side have created the better chances, but having come close on a couple of occasions were unable to get the breakthrough.
Birmingham started well, with Ravel Morrison and Nathan Redmond causing the Leeds defence problems. Morrison in particular had a couple of half-chances, before striking the crossbar with a curling effort on 14 minutes.
They went close again five minutes later when Shane Ferguson's 30-yard effort missed the post by inches.
Morrison went close again just before half time, beating his defender on the edge of the box before firing just wide with a powerful effort.
The home team couldn't find the goal though, and the sides remain level.