I respectfully disagree with Cthulhu's opinion. If they avert their eyes however while in statue form, then only have a 50% chance each round of having to make a saving throw. I'd say if they are in statue form the the Basilisk is just walking around where they are they wouldn't notice they were actually alive. They have an Int of 2, not exactly smart. I doubt they'd even look at them, in which case I wouldn't even require a save.