Raw nuts in their shell do not require Passover certification.
Shelled nuts that list BHA or BHT (preservatives) in the ingredients require special Passover certification. They are sprayed on the nuts using corn derivatives (kitniyot). If no additives are added, they may be used without special Passover certification.
In Europe different communities had different customs about peanuts. Some held them to be kitniyot; while others ate peanuts on Passover.
Many years ago the OU certified Kosher for Passover peanut oils for those Jews whose custom was to eat peanuts and peanut oil on Passover.
However, in recent years we have stopped certifying peanut oil as Kosher for Passover.
Furthermore, we cannot recommend that people whose custom is to use peanut oil on Passover use un-certified peanut oil, because of concerns about the peanut oil being processed on non-Passover equipment.