In my PCB layout design, I'm using a 40 mil width trace (shown in green in the image below) to carry 5V from a USB connector to the rest of the circuit. There is a test point for this net (marked with a blue arrow), and my question is: Should I reduce the trace width at the test point branch?

 

If that is just a test point, there is no current flow, and the trace width does not matter.
Often in CAD the "+5V" net gets declared power and width=40. The program will try to force all widths to 40 for that net. Not having 40 will cause an error when you check the board. If you did not force all +5V=40mil then it does not matter.
IMO do what you want.

 

Thanks!