Answer: I can't positively diagnose the problem without examining the tree so I can only offer some observations. Water stress and overfertilization can cause the symptoms you describe, as can a fungal disease called verticillium wilt. This disease is more common in maples but can affect many different trees and shrubs, including Katsura. There seem to be two forms of the disease, one in which plants die slowly over several years and another where they die rapidly within a few weeks. Trees that show minor branch wilt one year may show more the next year or may not show symptoms again for several years. There is some evidence that unbalanced fertilization (too much or too little nitrogen, for example) exacerbates this disease. Verticillium produces greenish streaks; in smoke-tree, the streaking is yellow-green. In other woody plants, the discoloration is brown. This makes identification difficult. The appearance of streaking helps to identify the disease but does not guarantee that the tree has Verticillium. Sometimes other factors or diseases cause discoloration of sapwood. Only laboratory examination can positively diagnose the disease. Out of curiosity, though, I think I would cut a pencil thick branch and inspect the wood. Streaking in the wood might indicate presence of verticillium. A final consideration is leaf scorch, which may simply be normal for your Katsura. If the tree is valuable you may want to hire a certified arborist to come out and inspect the tree.
Wish I had more information to share. Best wishes with your tree.
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