My personal preference is to ground the coax shield regardless of whether the antenna is mounted in the attic or outdoors. In the case of the attic install you have no significant risk of a lighting strike, but you would still want the circuit breaker to trip if power came in contact with the coax. (It has happened... A nail or screw driven into a wall, resulting in damage to power and TV cables for example.)
If you have a splitter in the system, it likely has a connection lug for a ground lead. A cheap and easy step for most installations.
http://forum.tvfool.com/showthread.php?t=901