Q.Can the top of a very small Crape Myrtle be trimmed?
The tree is alive but but the top of the main stem looks brown other spots clearly look green. I’m wondering if it’s possible that just a portion is dead and that I can cut it so that it isn’t going to cause any harm to the very small tree. Also it is healing from leaf spot not sure if that has anything to do with why that top part has died. Any advice is greatly appreciated.

Certified GKH Gardening Expert
There are many blights and fungal infections common to the state. It is likely what is going on here. Cutting dead portions of the shrub can be done at any time, but you will also need to treat the issue in order for this to not happen again.
Fungicides should be used on the upper portions of the shrub. This article will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
You can also apply DOLOMITIC LIME and WETTABLE SULFUR to the soil once or twice per year. This will help condition the soil, and prevent and kill future infections.
This article will help you to grow Crape Myrtles properly: https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-care.htm