The NEC doesn't require an attic antenna to be grounded. However, from my personal experience, I suggest that the coax be grounded with a grounding block that is connected to the house electrical system ground with 10 gauge copper wire.
If one of the runs of coax is connected to a piece of equipment that has a 3-wire power cord connected to a good 3-wire outlet, that would probably be sufficient.
I'm concerned about personal electrical safety. All AC operated equipment has leakage current, even when operating properly. Just because you can't feel it, doesn't mean it isn't there. If any piece of equipment becomes defective, you would be protected from shock.
I have had three close calls with shock, so I'm probably more concerned than most people. I learned about leakage current when I was doing a calibration test of a converter box for a friend, and felt a mild shock. I couldn't rest until I found out why.
Here is another case of potential leakage current shock from equipment that was operating properly:
http://www.digitalhome.ca/forum/81-o...ml#post1457594
http://www.digitalhome.ca/forum/81-o...ml#post1457668