Of course.
If it has an attack roll, it can score a critical threat. If you confirm that, it is a critical hit. If it doesn't have a threat range or multiplier listed, you use 20/x2 as the default.
When you make an attack roll and get a natural 20 (the d20 shows 20), you hit regardless of your target's Armor Class, and you have scored a "threat," meaning the hit might be a critical hit (or "crit"). To find out if it's a critical hit, you immediately make an attempt to "confirm" the critical hit—another attack roll with all the same modifiers as the attack roll you just made. If the confirmation roll also results in a hit against the target's AC, your original hit is a critical hit. (The critical roll just needs to hit to give you a crit, it doesn't need to come up 20 again.) If the confirmation roll is a miss, then your hit is just a regular hit.
A critical hit means that you roll your damage more than once, with all your usual bonuses, and add the rolls together. Unless otherwise specified, the threat range for a critical hit on an attack roll is 20, and the multiplier is ×2.
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Spells and Critical Hits
A spell that requires an attack roll can score a critical hit. A spell attack that requires no attack roll cannot score a critical hit. If a spell causes ability damage or drain (see Special Abilities), the damage or drain is doubled on a critical hit.
I snipped out some of the extra stuff in the middle.
That last bit talks about spells, but there is nothing anywhere to say not to apply it to identical ability damage or drain caused by non-spells (such as the touch of a Shadow), and the first part about "when you make an attack roll" is all inclusive: ALL attack rolls.
On a side note, few things give me more pleasure than to see a Shadow throw down a confirmed critical hit on a STR-dumped dervish dancer. Yeah, make those SAD characters. Come on. I dare you...
Nothing against martials; I love turning wizards and sorcerers and gunslingers and, well, any STR-dumped, "Hey barbarian, will you carry my backpack for me because I'm too feeble to lift it myself" loser adventurers into shadows and then turning them on their former companions and watching them all die in horror as they realize (too late) that carrying that guy's backpack might have been a sign that there was a fatal flaw in this group of tough (but feeble) adventurers...
Bwu ha ha ha ha ha!
All true, Joesi. But on average, you won't see very many 12-point crits from your basic shadow. That's just a 1 in 36 chance. Could happen, but it's far more likely to do less than 10 STR damage. Statistically, 44.44% of all shadow crits will be between 6-8 damage, while exactly 2/3 will be in the range of 5-9 and exactly 5 out of 6 will be in the range of 2-9. None of those will one-shot anybody who did NOT dump STR.
Greater shadows are worse with d8 damage instead of d6, but even their average crit does only 9 STR damage, not quite enough to one-shot a normal (not dumped) STR.
Of course, anyone can get unlucky rolls. But there are just as many lucky rolls on those dice, and based on statistical averages, un-dumped STR should survive two hits or one crit most of the time, even from a greater shadow.