Just finished a game in which my V Radioactive Man rolled a crit miss while using the free action granted to the laser turret to make a ranged attack... With no judges around, we unanimously decided that RM takes the damage.
My RM and my opponent's V Beetle were the last two figs on the battlefield, and I lost as a result of the roll and ruling.

Just wondering what the "official" ruling would be...

Nothing happens when the Laser Turret crit misses. It is the turret that made the attack, not the character who activated it. And 1 damage to an object (if it even takes it) isn't enough to damage it.

The Laser Turret is making the attack, so it takes the crit miss damage. Since it's only one damage, nothing happens to the Laser Turrent

The character on the turret does not take a click from a turret critical miss. The turret is the one with the action, so it takes the damage. Since critical miss results in one click and it takes three to destroy an object, the net result is no effect.

It is the same for mystics. If the turret damages a figure with Mystics, nothing happens to the turret or the figure on it.

Thanks, all. It didn't make sense to give RM crit miss damage when he wasn't the one making the attack...