Hi, 

Your redbud tree could be suffering from drought stress. We’ve had a hot and relatively dry summer in Franklin County. It looks like the leaves are cupped or curling up which is a sign of heat/water stress. It is odd that only two branches seem to show that stress and their leaves turned brown. However, in urban settings it is not unusual to have some limbs of the redbud die back. See the note about redbud decline in this write by the Ohio Department of Natural Resources. https://ohiodnr.gov/discover-and-learn/plants-trees/broad-leaf-trees/redbud-cercis-canadensis 

My recommendation is to water the tree. This University of Minnesota link provides a good guide on how much to water and what factors to consider. https://extension.umn.edu/planting-and-growing-guides/watering-established-trees-and-shrubs#measuring-tree-root-spread-1261762 

Another consideration is to trim out the affected limbs. However, before you do that, scratch the bark. If it is still green the limbs are still alive. 

From the images, I cannot tell if there are other factors, such as pests or disease, affecting your tree. If you would like to send a limb sample (dead and alive) to Ohio’s 
plant and pest diagnostic clinic, here is a link to the site. You will need to go to several drop down menus to see how to submit a sample etc. https://ppdc.osu.edu/ also send as much information as possible about the tree, location, age, whether it gets watered etc. 

General info on redbud trees including liking to be regularly watered. https://plants.ces.ncsu.edu/plants/cercis-canadensis/

I hope this information is helpful. 

Sabine