Thanks for your question. It is common for redbud to have branch dieback after winter, especially in Iowa, which is at the northern edge of its native range.  Occasionally the dieback is from winter damage.  

Another reason for branch dieback is vascular disease.  Verticillium wilt is one example of a vascular disease that is common on trees like redbud that can cause branch dieback.  

The best way to determine if it is verticillium wilt is to submit a sample to the Plant and Insect Diagnostic Clinic. If you do not wish to do that (don’t have a sample, don’t want to wait for a diagnosis, don’t want to pay the fee, etc.), there is one thing you can do that can help confirm the possibility of verticillium wilt and that is look for vascular streaking in the stem.

More information of how to check for vascular streaking and photos of what it looks like can be found here:

https://store.extension.iastate.edu/Product/12187 (click the “download” button in the center of the page to download and open the free pdf file)

https://hortnews.extension.iastate.edu/1998/3-13-1998/verticil.html

https://hortnews.extension.iastate.edu/verticillium-wilt

If you wish to send in a sample, instructions for how to collect and send in a sample for testing are in the third link provided above.

If further investigation shows that its likely verticillium wilt or if the sample comes back positive, note that no fungicides are effective against Verticillium wilt. If symptoms are not widespread, individual dead branches should be pruned, but be sure to disinfect (such as with a 10% household bleach solution) pruning tools between cuts.  Be sure to dispose of the dead branches so they do not potentially re-infect the tree.

Canker is another potential cause for branch dieback like this.  Canker is a fungal disease that typically causes discolored, often sunken spots on the stems and branches with the branches dying beyond that lesion/spot.  As with Verticillium wilt, the best way to determine if it is a canker disease is to submit a sample to the Plant and Insect Diagnostic Clinic.  More information about cankers can be found here: 

https://hortnews.extension.iastate.edu/cytospora-canker

https://store.extension.iastate.edu/Product/6197 (click the “download” button in the center of the page to download and open the free pdf file)

I would advise further investigation to see if canker or verticillium wilt is a potential cause for this dieback utilizing the resources above. If disease is not the cause or based on observations doesn’t seem likely, the issue is probably cultural or environmental. I suspect winter die-back.  Continue to provide good consistent care for the tree and it should grow out of the issue.

I will need more information about the neighbors tree to comment on its health. I didn't see any photos of that tree and it is not clear what symptoms it is experiencing.

Happy gardening!