Do critical hit bonuses apply to staves?

I've decided I want to play a mage in Kingdoms of Amalur: Reckoning. However, during the character customization, I wasn't expecting to play a mage, so I chose the +crit chance/+crit damage power. Now I'm wondering,

Does this critical chance apply to the base attack with staves as well as normal melee weapons? Particularly when the staff doesn't have "Physical" or "Piercing" damage?

Yes, you get critical hits with Staves (and Scepters and Chakrams) as a Mage and gems, DIY sagecraft builds or other Crit bonuses will increase the Damage and/or Frequency of critical hits.

Generally speaking, esp. with Staves/Scepters, you will NOT get physical bonuses. You WILL get physical bonuses with Chakrams, my work-a-day Mage Weapon.

Piercing, Bleeding bonuses are a no-go for most Mage-specific weapons as well.

Keep in mind that as opposed instead of a Finesse-type or Might-type character your Sorcery-type character will be inflicting (most) critical hits with Magic. So be on the look out for items that give you a "X% Critical Hit Damage with Magic" or just plain "X% Chance to Critical"

But you will do better with a Stave if you focus on technique instead hoping for criticals during 'button mashing.' The Stave is best as a slow masher: When attacking a single big baddie it's better to pause between button hits. HIT-breathe-HIT-breathe-HIT-breathe and then a quick bam-bam-bam with your melee weapon of choice. After all, the Stave is to the mage as the greatsword and hammer are to the Tank. It's for finish work and one-on-one fights -- not thinning the ranks. You'll want chakrams and advanced spells (lightning storm) for that.

Yes it does.

Source: Personal experience (I can add critical gems on staves when crafting them,which proves the fact that it applies,because if it wouldn't apply then the game wouldn't allow me to use critical gems when crafting staves).

While it is not a definitive answer, I am tempted to say - yes.

I have recently come across the following item:

The item in question has a bonus that appears to be a subset of the generic +X% chance bonus for critical hits, seeing how it specifically states that it applies only to physical damage. Making the very sensible assumption these two types of bonuses are actually different (and not just the same bonuses with different descriptions, one of which is lacking) then it is pretty safe to say that the general +X% chance bonus applies to any sort of damage.