Spell-Like Abilities: How do I know whether a spell-like ability is arcane or divine?
The universal monster rules for spell-like abilities states: "Some spell-like abilities duplicate spells that work differently when cast by characters of different classes. A monster's spell-like abilities are presumed to be the sorcerer/wizard versions. If the spell in question is not a sorcerer/wizard spell, then default to cleric, druid, bard, paladin, and ranger, in that order."
For spell-like abilities gained from a creature's race or type (including PC races), the same rule should apply: the creature's spell-like abilities are presumed to be the sorcerer/wizard versions. If the spell in question is not a sorcerer/wizard spell, then default to cleric, druid, bard, paladin, and ranger, in that order.
For spell-like abiities gained from a class, use the spell type (arcane or divine) of that class to determine whether the spell-like ability is arcane or divine. If the class doesn't cast spells, use the above rule for spell-like abilities from race or type.
Edit 7/15/13: Wording changed match the precedent in the universal monster rules for spell-like abilities.
Edit 9/23/13: Wording updated to clarify racial/type SLAs vs. class SLAs.