I am updating the main breaker box and want to sure everything is done properly according to the NEC. Can I run one ground wire (4) from the panel to the grounding rod and then another wire (4) from the grounding rod to the cold water pipe. Or, do I need to run a separate wire from the main panel to each independently? Rod is 5/8" and service will be 200 amp. Thank you in advance.
In the 2014 NEC handbook there is an exhibit 250.22 that shows this case. There is only 1 wire coming from the electrode to the panel. I would have said this would not be code compliant but it is clearly shown that the wire from the grounding electrode can run to the pipe saving a bunch of wire in some cases. Good Question!
The wire in question would simply be a bonding jumper and can be connected to the grounding electrode conductor to the rod.
Typically a connection to only a ground rod needs to be no larger than #6cu. You are running #4cu so you can do as you propose, since the connection to a water bond for 200A would require #4cu.
The wire from the panel to the rod must be continuous and without splice, but you can tap onto it using a split-bolt splice or similar connection. The wire from the grounding electrode conductor to the water pipe would now be considered a bonding jumper.