The American Opportunity or Lifetime Learning Credit can be claimed in the same year the beneficiary takes a tax-free distribution from a Coverdell ESA, as long as the same expenses aren't used for both benefits.
This means that qualified higher education expenses are reduced by
1) tax-free educational assistance (scholarships and grants), and
2)any expenses paid by a Coverdell ESA distribution
Any remaining expenses can then be used to calculate the American Opportunity or Lifetime Learning credit.
