In the Deluxe Edition RAW, there's no text specific to that. It does say that a character only goes Berserk if she fails a Smarts test.
From the Deluxe Edition:
- Smarts is a measure of how well your character knows his world and culture, how well he thinks on his feet, and mental agility.
- Spirit reflects inner wisdom and willpower. Spirit is very important as it helps your character recover from being Shaken.
I'd rule that Smarts tests are the only attribute tests that require concentration. Spirit, being more of a instictive/gut feeling kind of attribute, reflect your character's morals and will and as such doesn't require concentration.
That's not to say Spirit based skills don't require concentration - each action should be ruled by the GM based on common sense - hence the deliberately vague rules on the matter.